Areas Related To Cricles - Class 10 Maths - Extra Questions

Find the circumference (in cm) of a circle whose radius is 42 cm.



Length of an arc of a sector of a circle with radius r and angle with degree measure $$\theta$$ is $$\displaystyle \frac{\theta}{360} \times m\pi r$$
$$m$$ is



Take $$\pi = 3.14$$, the circumference of a circle with diameter = 1.2 m is 3.768 m.

If true then enter $$1$$ and if false then enter $$0$$.



If the area of a circle is 154 $$cm^2$$, then its circumference in cm is



Take $$\pi = 3.14$$, the circumference of a circle with radius $$= 6$$ cm is $$37.68$$ cm
If true then enter $$1$$ and if false then enter $$0$$.



A roller has a diameter of 14 m, then find its circumference in m



A sector of a circle with radius $$10\, \mathrm {cm}$$ has central angle $${72}^{o}$$. Find the area of the sector. $$\left(\pi = 3.14\right)$$



Find the area of the sector of a circle with radius $$6$$ $$cm$$ and the length of arc is $$15$$ $$cm$$



A horse is tied with a rope of length $$28$$ metre. Calculate the grass which can be grazed by the horse.



A sector of a circle with radius $$18\;\text{cm}$$ has central angle $${120}^{\circ}$$. Find the area of the sector. Use $$ \pi = 3.14$$



A sector of a circle with radius $$20$$ $$cm$$ has central angle $${90}^{o}$$. Find the area of the sector. $$\left( \pi = 3.14\right)$$.



Find the area of sector of a circle with radius $$4\ cm$$ and angle $$30^{o}$$. Find the area of corresponding major sector, $$(\pi =3.14)$$



Find the area enclosed  by each of the given figures:
1165918_1a04b0e32d854a54a5c3b91dd252729d.png



Find the area of a quadrilateral $$ABCD$$
1165732_2cf0d06605204dba8bd1cf85143241f0.png



Find the area of sector of a circle with radius $$4cm$$ and of angle $${30}^{o}$$



From a circle with radius $$21\ cm$$ a sector is cut off for which the measure of the angle at the centre is $$150$$. Find the length of the arc of that sector and also find the area of the sector.



Find the angle subtended at the centre of the circle by an are whose length is $$15\ cm$$ if the radius of the circle is $$25\ cm$$.



In a circle, an arc of length $$4\pi\ \text{cm}$$ subtends an angle of measure $$40^{\circ}$$ at the centre. Find the radius of the circle and the area of the sector corresponding to that arc.



Find the area of the shaded parts of the given figure.
1173228_55962087c392430cb4c03059c8ea59c5.png



On a circular table top of radius $$30cm$$ a design is formed leaving an equilateral triangle inscribed in a circle. Find the area of the design.($$\pi3.14$$)



$$AB$$ and $$CD$$ are respectively arcs of two concentric circles of radii 21$$\mathrm { cm }$$ and 7$$\mathrm { cm }$$ with centre $$\mathrm { O }$$ . If $$\left\lfloor A O B = 30 ^ { \circ }\right.$$ .the area of the shaded region.
1223237_ededa703cd0f4d1ea1b86510b841d9dd.png



Four circular cardboard pieces of radii $$7\mathrm { cm }$$ are placed on a paper in such a way that each pieces  touches the other two. Find the area of the portion enclosed between these pieces.



Find the area of following shape. 
1267536_202e9a7202354e988e33be0ea1293526.PNG



Find the area of sector of a circle with radius $$6\ cm$$, if angle is $$60^{o}$$.



If the radius of the circle is $$6\ cm$$ and the length of an arc is $$12\ cm$$, find the area of the sector.



Find the area of the shaded region form figure, if the diameter of the circle with centre $$O$$ is $$28\ cm$$ and $$AQ=\dfrac{1}{4}AB$$.
1279549_ab3b6eb659034a74bfa06873dd4b2178.png



Four equal circles are described about the four corners of a square so that each circle touches two of the others. Find the area of the space enclosed between the circumferences of the circles, each side of the square measuring $$24\ \mathrm{cm}$$.



In the given figure, ABCD is a trapezium of area $$24.5{ cm }^{ 2 }$$. If $$AD\parallel BC,\angle DAB={ 90 }^{ 0 },AD=10cm,BC=4cm$$ and $$ABE$$ is quadrant of  circle then find the area of the shaded region.
1378879_1120a5170a534593825365c0046955e9.png



In quadrilateral $${\text{ABCD}}$$ shown in figure, $${\text{AB}}\parallel {\text{DC}}\;{\text{and}}\;{\text{AD}} \bot {\text{AB}}$$, Also $${\text{AB = 8m,}}\;{\text{DC = BC = 5m}}{\text{.}}$$ Find the area of the quadrilateral.
1249965_8a1ae366e2124d118d9b3dbdd05a97e0.PNG



Find the area (in $$cm^{2}$$) of the circle that can be inscribed in a square of side $$8\ cm$$.



The adjoining figure represents a rectangular lawn with a circular flower bed in the middle.
Find the circumference of the flower bed.
1646618_7f6119a227ec4183917eca894835d586.png



In the following figures, find the area of the shaded portion.
1646619_d0f50df56cbc44a7a6705f4d1d86aa7e.png



Four horses are tethered with equal ropes at 4 corners of a square field of side 70 meters so that they just can reach one another . Find the area left ungrazed by the horses.



If the radius of a circle is 7 cm and the central angle is $$60^{\circ}$$, Find the length of the arc.



From the top of the mast of ship, which is $$66$$ feet above the sea , the light of a lighthouse which is known to be $$132$$ feet high can just be seen ; prove that its distance is $$24$$ miles nearly 



Prove that, if the height of the place of observation be n feet, the distance that the observer can sec is $$\sqrt{\dfrac{3n}{2}}$$ miles nearly.



The area of sector with angle $$45^{\circ}$$ of a circle with area as $$250cm^2$$.



The diagram shows a sand pit in a child's play are. The shape of the sand pit is a sector of a circle of radius 2.25m and sector angle $${ 56 }^{ 0 }.$$ Calculate the area of the a sand pit. 
1449051_e4eb8ae4882a45449b761d8b228c7459.PNG



The adjoining figure represents a rectangular lawn with a circular flower bed in the middle.
Find the area of the whole land.
1646615_e3cb16ec9a3d45c280514ea5f81a0ad7.png



Find the area of the shaded portion in the following figures.
1794566_4f3eba13ec644c10a13f891f441128cf.png



What do you understand by a plane closed figure?



The interior of a figure is called region of the figure, Is this statement true?



The area of a circle is 1386 sq. cm, find the value of its circumference. 



Find the angle in degree subtended at the centre of a circle by an arc, for the given,  
$$\displaystyle radius \: of \: circle = 5.5m, \:length \: of \: arc = 6.05m\left [ \pi =\frac{22}{7} \right ]$$



The diameter of a circle is $$10$$ cm. Find the length of the arc, in cm, (nearest integral value), when the corresponding central angle is $$45^{\circ}$$.



Find the angle in degree subtended at the centre of a circle by an arc, for the given, 
$$\displaystyle radius \: of \: circle = 20cm, \:length \: of \: arc = 78.50cm\: (\pi =3.14)$$



An ant is moving around a few food pieces of different shapes scattered on the floor. For which food piece would the ant have to take a longer round?
463319.png



If two chords $$AB$$ and $$CD$$ of a circle $$AYDZBWCX$$ intersect at right angles prove that $$arc (CXA) + arc (DZB )= arc( AYD )+ arc( BWC )= arc(\text{semicircle})$$


426712_9bf07ee6865f4817bf9b9d161e41d24e.png



A chord of a circle of radius $$15\ cm$$ subtends an angle of $$60^{\circ}$$ at the centre. Find the areas of the corresponding minor and major segments of the circle.
(Use $$\pi = 3.14$$ and $$\sqrt {3} = 1.73$$)



A horse is tied to a peg at one corner of a square shaped grass field of side $$15 m$$ by means of a $$5 m$$ long rope. Find
(i) the area of that part of the field in which the horse can graze.
(ii) The increase in the grazing area if the rope were $$10 m$$ long instead of $$5 m$$. (Use $$\pi = 3.14$$)
465216_7097c50187264d8c81300622fb8458c0.png



Find the area of a sector of a circle with radius $$6\ cm$$ if angle of the sector is $$60^{\circ}.$$



A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends .The length of the entire capsule is $$14\ mm$$ and the diameter of the capsule is $$5\ mm$$. Find its surface area. (Use $$\pi = \dfrac{22}{7}$$).




A brooch is made with silver wire in the form of a circle with diameter $$35\ mm$$. The wire is also used in making $$5$$ diameters which divide the circle into $$10$$ equal sectors as shown in fig find:

(i) The total length of the silver wire required.

(ii) The area of each sector of the brooch

465219_53b558036eb74180927251455b51d413.png



Find the area of the shaded region in fig., if $$PQ = 24\ cm,\ PR = 7\ cm$$ and $$O$$ is the centre of the circle.
465229_b3117d79270b44098577210d8f6bbe4a.png



A chord of a circle of radius $$12\ cm$$ subtends an angle of $$120^{\circ}$$ at the centre. Find the area of the corresponding segment of the circle. (Use $$\pi = 3.14$$ and $$\sqrt {3} = 1.73$$)



A car has two wipers which do not overlap. Each wiper has a blade of length $$25\ cm$$ sweeping through an angle of $$115^{\circ}$$. Find the total area cleaned at each sweep of the blades



To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $$80^{\circ}$$ to a distance of $$16.5\ km$$. Find the area of the sea over which the ships are warned. (Use $$\pi = 3.14$$)



In given figure the area of an equilateral triangle $$ABC$$ is $$17320.5\  cm^{2}.$$ With each vertex of the triangle as a center, a circle is drawn with a radius equal to half the length of the side of the triangle. Find the area of the shaded region. (Use $$\pi = 3.14$$ and $$\sqrt {3} = 1.73205$$)
465240_1c771cac7766406fa63ef60486437089.png



In fig., $$ABCD$$ is a square of side $$14\ cm$$. With centers $$A, B, C$$ and $$D$$, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region
465237_6ada388fb30b4ef7bf23cf618a874850.png



Find the area of the shaded region in fig, where is circular arc of radius $$6\ cm$$ has been drawn with vertex $$O$$ of an equilateral triangle $$OAB$$ of side $$12\ cm$$ as centre
465233.PNG




In a circular table corner of radius $$32\ cm$$, a design is formed leaving an equilateral triangle $$ABC$$ in the middle as shown in Fig. Find the area of the design.
465236_b45ecce6ae284dbfa0e8077349c55e7d.png



Find the area of the shaded region in Fig., if ABCD is a square of side $$14 cm$$ and $$APD$$ and $$BPC$$ are semicircles.
465231_6e4b3aa3e84347529245e30bd6340c74.png



From each corner of a square of side $$4\  cm,$$ a quadrant of a circle of radius $$1\  cm$$ is cut and also a circle of diameter $$2\  cm$$ is cut as shown in figure. Find the area of the remaining portion of the square.
465235_2d358851108e489aa13831f4644d9ba2.png



Find the area of the shaded region in figure, if radii of the two concentric circles with center $$O$$ are 7 cm and 14 cm respectively and $$\angle AOC = 40^{\circ}$$.
465230_a851778565364ccfabd1306586145af1.png



In fig., $$AB$$ and $$CD$$ are two diameters of a circle (with centre $$O$$) perpendicular to each other and $$OD$$ is the diameter of the smaller circle. If $$OA = 14\ cm$$, find the area of the shaded region
465239_f03a221853b249e3b1d928f72ca770d4.png



The square water tank has its sides equal to $$20 m$$. There are four semi-circular grassy plots all round it. Find the area of semi-circular plots.



What is the length of an arc of a semicircle?

477278.PNG



Find the area of the shaded part in the figure. (Use $$\pi = 3.14$$)

477267_9b80f3c84b48492dbb3e937541c791ff.png



Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions $$14\ cm \times 7\ cm$$. Find the area of the remaining card board. $$\left[ \text{Use} \,\,\, \pi = \dfrac{22}{7} \right]$$



In Figure, two concentric circles with centre O, have radii $$21cm$$ and $$42 cm$$. If $$\displaystyle \angle AOB={ 60 }^{ \circ  }$$, find the area of the shaded region. [Use $$\displaystyle \pi =\frac { 22 }{ 7 } $$]

494193.png



In the figure, $$O$$ is the centre of a circle such that diameter $$AB = 13$$ cm and $$AC = 12$$ cm. $$BC$$ is joined. Find the area of the shaded region. (Take $$\displaystyle \pi =3.14$$).
494148_2c9df096af614ed4ae05212a3a53ce2d.jpg



In the following figure, PQRS is square lawn with side $$PQ = 42$$ meters. Two semi-circular flower beds are there on the sides PS and QR with center at O, the intersections of its diagonals. Find the total area of the two flower beds (shaded parts).
494314.JPG



In the figure, find the area of the shaded region, enclosed between two concentric circles of radii $$7$$ cm and $$14$$ cm where $$\displaystyle \angle AOC={ 40 }^{ \circ  }.$$ Consider $$\pi =\dfrac { 22 }{ 7 }.$$
494151.png



Find the area of the minor segment of a circle of radius 14 cm, when its central angle is $$60^o$$. Also find the area of the corresponding major segment. $$\displaystyle \left[ Use \,\,\, \pi = \frac{22}{7} \right]$$



In the given figure, $$ABCD$$ is a rectangle and three circles are positioned as shown. Find the area of the shaded region, rounded to the nearest $$\displaystyle { cm }^{ 2 }$$.
528280.JPG



Find the value of $$x, y$$ in given figure for which the lines $$AD$$ and $$BC$$ become parallel.
570830_3a0648a1831a477ba112ee57a99828a3.png



Find the area of the sector whose arc length ad radius are $$12\ cm$$ and $$4\ cm$$ respectively



Find the area of sector of circle having radius $$6$$ $$cm$$ and length of the arc $$15$$ $$cm$$.



Find the area of the sector of a circle with radius $$4\ cm$$ and of angle $$60^{\circ}$$. Also find the area of the corresponding major sector.
(Use $$\pi = 3.14$$)



In the following figure, the radius of the circle is $$7$$ cm and $$m(arc RYS) = 30^{\circ}$$, find find:
$$A(P-RYS)$$
599379.png



Find the area of the shaded region in given figures
565480_772afa5ecd1f40038edee3375e0f36fa.png



Calculate the area of shaded part of the above figure.
565448_69438f4d1d924fb3a2a52b592335463d.png



A sector of a circle with radius $$12 $$ $$cm$$ has central angle $${60}^{o}$$. Find the area of the sector. $$\left( \pi =3.14\right)$$.



Find the area of shaded region of the figure given below
565465_f57055ffd8a04ba6a4e320668cd93fb6.png



Find the area of the shaded region shown in the figure. The four corners are quadrants. At the centre, there is a circle of diameter 2 cm.
616611_59d16c84769a4caa90355e2bd5d72318.png



In the given figure, ABCD is a square of side 14 cm. Find the area of the shaded portion.
616529_9cd6283c007d43a0a1afe668beb97c15.jpg



Find the area of the coloured regions
616607_acc279fb655a40bd91679a26767668b5.png



A chord of a circle of radius $$10\ cm$$ subtends a right angle at the centre. Find the area of the corresponding (i) Minor segment, (ii) Major segment. (use $$\pi = 3.14$$)



A horse is tethered to one corner of a rectangular field of dimensions 70 m by 52 m by a rope 28 m long for grazing. How much area can the horse graze inside? How much area is left ungrazed?
616525_2ed7a3293c964be09da13db8db8b806c.jpg



A pendulum swings through an angle of $$30^o$$ and describes an arc length of $$11$$ cm. Find the length of the pendulum.



A sector containing an angle of $$120^{\circ}$$ is cut off from a circle of radius $$21$$ cm and folded into a cone by joining the radii. Find the curved surface area of the cone. $$\left (\pi = \dfrac {22}{7}\right )$$



 Find the area of the shaded portions in the figure, where ABCD is a square of side 7 cm.
616584_96f71171b79740298fc6e24384c5a63d.jpg



A square park has each side of 100 m. At each corner of the park there is a flower bed in the form of a quadrant of radius 14 m as shown in the figure. Find the area of the remaining portion of the park.
616610_95f96e82002e4b41ba0f6b65eb99fd9f.jpg



The length of arc of a sector is 22 cm and its radius is 10.5 cm. Find its central angle.



In the given figure, $$\triangle ABC$$ is right-angled at $$A$$. Semi circles are drawn on $$AB, AC$$ and $$BC$$ as diameters. It is given that $$AB=3\ cm$$ and $$AC=4\ cm$$. Find the area of the shaded region in $$cm^2$$.
627768_1f1d22b84c2d43cbb20fb1e94007cebc.png



In a circle an arc subtends an angle $${45}^{o}$$ at the centre. If the length of arc is $$11cm$$ then find the radius of circle.



Calculate the area and perimeter of a quadrant of a circle of radius $$21$$ cm.



A toy is a combination of a cylinder, hemisphere, and a cone, each with a radius of $$10$$ cm as shown in the figure. The height of the conical part is $$10$$ cm and the total height is $$60$$ cm. Find the total surface area of the toy.

625045_31c6605eb30b40c9b868854561e3ae09.png



Find the perimeter of a sector whose radius and central angle are $$18$$ cm and $$210^o$$ respectively.



The length of a side of a square field is 20 mtr. A cow is tied at the corner by means of a 7 mtr long rope. Find the area of the field which cow can graze. If the length of rope is doubled then find the increase in the grazing area.



The area of sector is $$1540sq.cm$$. The sector subtends $${50}^{o}$$ at centre, then find the radius of circle.



If the perimeter and radius of a sector are 38 cm and 9 cm respectively, find its area.



The area of a sector of a circle of radius 14 cm is $$77 cm^2$$. Find its central angle.



In the given figure, $$ABC$$ is a right triangle, $$\angle B = 90^{\circ}, AB = 28\ cm$$ and $$BC = 21\ cm$$. With $$AC$$ as diameter a semicircle is drawn and with $$BC$$ as radius a quarter circle is drawn. Find the area of the shaded region.
870290_1a419b7b83104d2b9f7ea6d2203a70d8.png



Find the angle subtended at the centre of a circle of radius $$5$$ cm by an arc of length $$(\dfrac{5\pi}{3})$$ cm.



A sector of a circle of radius $$4\text{ cm}$$ contains an angle of $$30$$ $$^{\circ}$$. Find the area of the sector.



A horse is placed for grazing inside a rectangular field $$40$$ m by $$36$$ m and is tethered to one corner by a rope $$14$$ m long. Over how much area can it graze? (take $$\pi$$$$ = \dfrac{22}{7}$$).



The given figure shows a rectangle ABCD inscribed in a circle as shown alongside.
If AB=28 cm and BC=21 cm, then find the area of the shaded portion of the given figure.
851563_ed11c412c4ff4d3a92c916541a360895.png



A chord subtends an angle of $$120^{\circ}$$ at the centre of a circle of radius $$12\ cm.$$ Find the area of corresponding segment of the circle. $$\bigg(\dfrac {22}{7} = 3.14$$ and root $$3 = 1.73\bigg)$$



An arc of length $$20 \pi$$ cm subtends an angle of $$144$$ $$^{\circ}$$ at the centre of a circle. Find the radius of the circle.



An arc of length $$15$$ cm subtends an angle of $$45$$ $$^{\circ}$$ at the centre of a circle. Find in terms of $$\pi$$ ,the radius of the circle.



Find the angle subtended at the centre of a circle of radius $$'a'$$ by an arc of length $$(\dfrac{a\pi}{4})$$ cm.



AB is a chord of a circle of centre O and radius $$4 cm$$. AB is of length $$4 cm$$. Find the area of the sector of the circle formed by chord AB.



The minute hand of a clock is $$10$$ cm long. Find the area of the face of the clock described by the minute hand between $$8$$ am and $$8.25$$ am.



The perimeter of a sector of a circle of radius $$5.7\ m$$ is $$27.2\ m$$. Find the area of the sector.



Area of a sector of a circle of radius $$36\ cm$$ is $$54 \pi\ cm^{2}$$. Find the length corresponding arc of the sector.



A sector of $$56^{\circ}$$ cut out from a circle contains area $$4.4 \ cm^2.$$ Find the radius of the circle.



The perimeter of a certain sector of a circle of radius $$5.6$$ m is $$27.2$$ m. Find the area of the sector.



In a circle of radius $$35 cm$$, an arc subtends an angle of $$72$$ $$^{\circ}$$ at the centre. Find the length of the arc and area of the sector.



A sector of a circle of radius $$8\ cm$$ contains an angle of $$135$$ $$^{\circ}$$. Find the area of the sector.



A chord PQ of a length 12 cm subtends an angle of $$120^{\circ}$$ at the center of a circle. Find the area of the minor segment cut off by chord PQ.



A chord of a circle radius $$14$$ cm makes a right angle at the centre. Find the areas of the minor and major segments of the circle.



A plot is in the from of a rectangle ABCD having semi-circle on BC as shown in given figure. If $$AB = 60$$ m and $$BC = 28$$ m, find the area of the plot.
973449_c436384ff993438699721a86335d121b.png



Four equal circles, each of radius $$5$$ cm touch each other. Find the area included between them (Take $$\pi$$ $$= 3.14$$).



The inside perimeter of a running track (shown Fig.) is $$400$$ m. The length of each of the straight portion is $$90$$ m and the ends are semi-circles. If the track is everywhere $$14$$ m wide,find the length of outer track. Also find the area of track.
973541_a0ed062858bd492fba66e8003ab4d60c.png



A play ground has the shape of a rectangle, with two semi-circles on its smaller sides as diameters, added its outside. If the sides of the rectangle are $$36$$ m and $$24.5$$ m, find the area of the playground. (Take $$\pi$$  $$= \dfrac{27}{7}$$).



A chord AB of a circle, of radius $$14$$ cm makes an angle of $$60^{\circ}$$ at the centre of the circle. Find the area of the minor segments of the circle.



Find the area of the circle in which a square of area $$64 \, cm^2$$ is inscribed. (Use $$\pi$$ $$= 3.14$$)



In a circle of radius 6 cm, a chord of length 10 cm makes an angle of 110$$^{\circ}$$ at the centre of the circle. Find the length of the arc AB.



In given figure, OE $$= 20$$ cm. In sector OFST, square OEFG is inscribed. Find the area of the shaded region.
973559_81d1355b602a40ea9809463112ac6f4c.png



Four cows are tethered at four corners of a square plot of side $$50$$ m as shown in figure. What area will be left ungrazed ?
973495_96104c513abd484e8d19dbd01b77f232.png



A chord $$10$$ cm long is drawn  in a circle whose radius is $$5\sqrt{2}$$ cm. Find area of both the segments.



The radius of a circle with centre O is $$5$$ cm (given figure). Two radii OA and OB are drawn at right angles to each other. Find the areas of the segment made by the chord AB (Take $$\pi \, = \, 3.14$$)
973635_72f5873f416b4d4fa3d10c6c28ade229.png



From a thin metallic piece, in the shape of a trapezium $$ABCD$$, in which $$AB\parallel CD$$ and $$\angle BCD  =  90^{\circ}$$, a quarter circle $$BEFC$$ is removed (see figure). Given $$AB = BC = 3.5\  cm$$ and $$DE = 2\ cm$$, calculate the area of the remaining piece of the metal sheet.
973678_7f94aaf214484c908c46d9cdcd746877.png



From a circular piece of cardboard of radius $$3$$ cm two sectors of $$90^{\circ}$$ have been cut off. Find the perimeter of the remaining portion narest $$100$$th centimeters. (Take $$\pi \, = \, \dfrac{22}{7}$$)



The area of a sector is one twelfth that of the complete circle. Find the angle of that circle.



In fig., an equilateral triangle ABC of side $$6$$ cm has been inscribed in a circle. Find the area of the shaded region. (Take $$\pi \, = \, 3.14$$)
973590_9a48710fffae451b8be2ad486160fea0.png



In the given figure $$O$$ is the centre of the circle with radius $$28\ cm$$. Find the area of the minor segment $$ASB$$.
973564_156d888b99af4527828893c370651413.png



Find the area of a shaded region in the given figure, where a circular arc of radius $$7$$ cm has been drawn with vertex A of an equilateral triangle ABC of side $$14$$ cm as centre. (Use $$\pi$$ $$= \dfrac{22}{7}$$ and $$\sqrt{3}$$ $$= 1.73$$).
973617_436cd2a0b1af4d729cb8af8ef8b5b8f2.png



In given figure, the square ABCD is divided into five equal parts, all having same area. The central part is circular and the lines AE, GC, BF and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find the perimeter of the part ABEF.
973605_ede24d39c8df47d990dd552d783b9671.png



A circle is inscribed in an equilateral triangle ABC with side $$12$$ cm, touching its sides. Find the radius of the inscribed circle and the area of the shaded part.
973584_0d54705d1ddb45aa8293290de4f5600d.png



In given figure, the square ABCD is divided into five equal parts, all having same area. The central part is circular and the lines AE, GC, BF and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find the circumference of the central part.
973602_25b3d6962e8e439b92f0033b6242cd25.png



In given figure, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region. (Use $$\pi \, = \, 22/7$$)
973843_8129b0620af148dc896fea005f80bf38.png



In a circle of diameter $$40\ cm$$ the length of a chord is $$20\ cm$$. Find the length of minor arc of the chord.



Find the area of shaded region?
1016222_86a7ee243d5c457f8de732a625d6af13.jpg



A vertical tower stands on a horizontal plane and is surmounted by a flagsataff of height $$5\ m$$. From a point on a ground, the angles of elevation of the top and bottom of the flagstaff are $${60}^{o}$$ and $${30}^{o}$$ respectively. Find the height of the tower and the distance of the point from the tower. (Take $$\sqrt{3}=1.732$$) 



In given figure, shows a kite in which BCD is the shape of a quardrant of a circle of radius 42 cm. ABCD is a square and $$\Delta CEF$$ is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.
973782_e16478e317024d96abdcb45b37190fdc.png



A right triangle, whose sides are $$15cm$$ and $$20cm$$ is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed (Use $$\pi =22/7$$)
1010681_66e75686beda49b98f87c26130c650b9.png



The arc of a circle of radius $$21 cm$$ subtends an angles of $$60^{ o }$$ at the center, find the length of the arc.(in cm) (Take $$\pi=22/7$$).



Shalini has to cut out circe of diameter $$1\dfrac { 1 }{ 4 } cm$$ from an aluminium strip of dimensions $$8\dfrac { 3 }{ 4 } cm$$ by $$1\dfrac { 1 }{ 4 } cm$$. How many full circles can Shalini cut? Also calculate the wastage of the aluminium strip.



Fig. 15.87, shows the cross-section of railway tunnel. The radius OA of the circular path is 2 m. If $$\angle AOB \, = \, 90^{\circ}$$, calculate the perimeter of the cross-section.
973704_95aa703aa3bf4a3ca2100925a306e09b.png



In given figure, ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semicircles are drawn as shown in the figure. Find the area of the shaded region.
973765_ae652a29cb9b47609ef66dd43ad5e585.png



A circular region touching all the four sides of a square of side $$2\ cm$$ is painted. Find the area of the region which is not painted 



Find the area of polygon $$ABCDEF$$, if $$AD = 18 \,cm, AQ = 14 \,cm, AP = 12 \,cm, AN = 8 \,cm, AM = 4 \,cm$$ and $$FM, EP, QC$$ and $$BN$$ are perpendicular to diagonal $$AD$$.
1076311_20b6f5a4f971405692fbc04658edc789.png



The perimeter of a sector of a circle, of area $$25\pi$$ sq. cms, is $$20$$ cms. Find the area of sector.



Find the area of the shaded portion as shown in the adjoining figure. The four corners are quadrants of circle and at the centre there is a circle.
1125696_39dfe25062c946a3b2154ab83d42dc9d.png



.
1056944_dac3a586e91d44f185dab3f9550f007c.PNG



The perimeter of a sector of a circle, of area $$64\pi$$ sq. cms, is $$56$$ cms. Find the area of sector.



Find the area of the polygon:
1114216_f4e2001f4b2844dd943bfe08abf27d3c.JPG



Find the area of a sectors of a circle with radius $$14cm$$,If the length of the corresponding arc is $$22cm$$?



In quadrilateral $$ABCD$$, angle $$D=90^{o}, BC=3\ cm$$ and $$DC=25\ cm$$. A circle is inscribe in this quadrilateral which touches $$AB$$ at point $$Q$$ such that $$QB=27\ cm$$ and BC = $$38$$ cm. Find the radius of the circle.



Find the area of the segment of a circle of radius $$14\ cm$$, if the length of the corresponding $$arc\ APB$$ is $$22\ cm$$



$$2$$ cubes of side $$8\ cm$$ are joined end to end. Find the length, breadth and height of resulting cuboid.



In the adjoining figure, $$ABCD$$ is a rectangle of size $$18\ cm$$ by $$10\ cm$$. In $$\Delta BEC,\ \angle E=90^{o}$$ and $$EC=8\ cm$$. Find the area of the shaded region. 
1128588_fb799c0406454d1896eb617e36b54d15.png



In the given figure a circle of radius $$7\ cm$$ is inscribed in a square, find the remaining area of the square.
1128728_f9bd563e389d4156899ade426e8fa6e2.png



In the adjoining figure, $$O$$ is the centre of a circle. The area of sector $$OAPB$$ is $$\dfrac {5}{18}$$ of the area of the circle. Find $$x$$
1128202_4a0d263ba9f34237a8189f16af7d6718.png



An arc of a circle of radius 14 cm subtends an angle of 60$$^{o}$$ at the centre. Find the area of the major sector.



The length of an arc of a circle is 4 cm and its radius is 6 cm. Find the area of this sector of the circle ?



Calculate the area of the designed region in figure, common between the two quadrants of circles of radius $$8\ cm$$ each.
1166017_7e4cd69c95884e939418628ae17ce5dd.png



Find the area of the segement of a circle of radius $$14\ cm$$. If the length of the corresponding are $$APB$$ is $$22\ cm$$.



A car wiper has two blades each of length $$56\ cm$$. How much area will they both sweep if each makes an angles of $$135^{o}$$ while it moves. $$[Use\ \pi=\dfrac {22}{7}]$$



$$AC$$ and $$BD$$ are two perpendicular diameters of circle $$ABCD$$. Given that, the area of the shaded portion is $$308\ cm^{2}$$. Calculate (i) the length of $$AC$$ and (ii) the circumference of the circle.

1165002_27ccf8e1c3764ecb825c95294f81fc3d.png



Find the area of both the segments of a Circle of radius $$43cm$$ with central angle $$120 ^ { \circ }.$$ [Given, $$\sin 120 ^ { \circ } = \dfrac { \sqrt { 3 } } { 2 }  { and } \sqrt { 3 } = 1.73$$]



A chord of a circle of radius $$10cm$$ subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment  (ii) major sector (Use $$\pi=3.14$$)



Find the area of the shaded region.
1164953_d3b64a3ad82a43e388a2003d7a6304b6.png



An umbrella has $$8$$ ribs which are equally spaced. Assuming umbrella to be a fat circle of radius $$45cm$$, find the area between the two consecutive ribs of the umbrella.



The minute hand of a clock is $$\sqrt{21}$$ cm long . find the area described by the minute on the face of the clock between 7.00 AM and 7.05 AM.



ΔLMNΔLMN
(2) Area of any one of the sectors.
(3) Total area of all the three sectors.
(4) Area of the shaded region.

1193717_ddbb0d9a53004509895d6dee4950b3b9.png



The perimeter of a sector of a circle of area $$25\pi\text{ sq. cm} $$ is $$20\text{ cm}$$. Find the area of the sector?



In figure, ABCDABCD, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region
1198365_a08827011d9640ac87780502549f3130.png



A chord $$PQ$$ of a circle of radius $$10 \mathrm { cm }$$ subtends an angle of $$60 ^ { \circ }$$ at the centre of the circle Find the area of major and minor segments of the circle.



Find the area of shaded region 
$$AC=BD=7cm$$
$$AB=CD=1.75cm$$
1196448_09dfed9548f84d21ac6c0b82cf99838b.png



Figure depicts a racing track whose left and right ends are semicircular.
The distance between the two inner parallel line segments is $$60\ m$$ and they are each $$106\ m$$ long. If the track is $$10\ m$$ wide, find:
(i) the distance around the track along its inner edge
(ii) the area of the track
1169869_cd3b93404b574d7fb3f1ecddd056fb2d.PNG



A circle of radius a is divided into 6 equal sectors. An equilateral triangle is drawn on the chord of each sector to lie outside the circle. Area of the resulting figure is:



A wire is in the form of an equilateral triangle with area $$\sqrt{3} m^{2}$$. If it is changed into a circle, the radius will be:



Find the length of an are of  circle which subtends an angle of $$180^0$$ at the centre, if the radius of the circle is $$15$$ cms.



Radha made a picture of an aeroplane with colored paper as shown in the figure. Find the total area of the paper used.
1202920_28a1895715054dee8b7f51a5f5e72aec.PNG



Find the area of the shaded region in figure.
1203089_4aac7bfae09b47bfaaf2b20e6fc59715.png



A circle inscribed in an equilateral triangle.If the circumference of the circle is $$176cm$$, find the area of the shaded region ?

1198501_5f411ff514c44587b47429761a2e9765.png



In the fig, find the perimeter of the shaded region, if $$ABCD$$ is a square of side $$21\ cm$$ and $$APB$$ and $$CPD$$ are semicircle.
1204178_a1195f731de047e696ddcd208ff3e12d.png



In the given figure, $$ABCD$$ is a trapezium of area $$24.5\;cm^2$$. If $$AD \parallel BC, \angle DAB=90^{\circ},AD=10\;cm,BC=4\;cm$$ and $$ABE$$ is quadrant of a circle. then find the area of the shaded region. 
1214739_bbead475d76c451facdf953e41ac135b.PNG



A path $$2.5$$m wide is running around a square field whose side is $$45$$m. Determine the area of the path.



In the above figure, a square is inscribed in a circle of diameter $$d$$ and another square is circumscribing the circle. Find the ratio of the area of the outer square to the area of the inner square. 
1226979_cda787a0f3f24a82a075d229424a322c.png



Radius of a sector of circle is $$3.5\ cm$$ and length of its arc is $$2.2\ cm$$. Find the area of the sector.



Find the area of the minor segment of a circle of radius $$42\ cm$$, if the length of the corresponding are is $$44\ cm$$.



Find the area of the segment AYB shown in figure, if radius of the circle is 21 cm and $$< AOB =120^0$$. $$\left(\ Use\ \displaystyle \pi=\dfrac{22}{7}\right)$$
1230433_0035bf3303f641299c39290d8df63fc1.png



A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends. The length of the entire capsule is  $$14\mathrm { mm }$$  and the diameter of the capsule is  $$5\mathrm { mm }.$$  Find its surface area. 
1219933_fc379fbdf0574f1fa579841bee98a0b1.png



Area of a sector of a circle of radius $$15\ cm$$ is $$30\ cm^{2}$$. Find the length of the arc of the sector.



In a circular table cover of radius $$32$$ cm. A design is formed leaving an equilateral triangle $$ABC$$ is the middle as shown it. Find the area if the design.  
1223295_86f72fa5f91849d69e7c4b12bf97d71b.png



From a rectangular metal sheet of size 20cm by 30cm, a circular sheet as big as possible is cut.find the area of the remaining sheet.



A window is in the shape of a rectangle surmounted by semi-circle. If the perimeter of the window is $$20\ ft$$, find the maximum area.



Adjoining fig, ABCD is a trapezium with $$AB\parallel DC$$ and $$\angle BCD=30^0.$$ Fig. BGEC is a sector of a circle with centre C and AB = BC = 7 cm, DE = 4 cm and BF = 3.5 cm, then find the area of the shaded region. $$(Use\quad \pi =\frac { 22 }{ 7 } )$$
1250967_55b5c632a9bf429e8d14660eea3157cd.PNG



Find the perimeter of the given shape (Fig) (Take $$\pi = \frac { 22 } { 7 } \}$$
1256067_29926514b1544ccc9740326f1bac947f.png



Two circular pieces of equal radii and maximum area, touching each other arc cut out from rectangular card board of dimensions $$14 cm\times 7 cm$$. Find area of remaining card board.



Find to three places of decimal of radius of circle whose area is sum of areas of two triangles whose sides are $$35,53,66$$ and $$33,56,65$$ in cms.



Find the area of the following figure whose dimensions are shown.
1241916_e0aae552ef804c1e96d3201e5e8d5180.png



A rectangle is $$22\ m$$ long and $$12\ m$$ wide.From its four corners,quadrants of radius $$2.5\ m$$ have been cut. Find the area of the remaining part.



The short and long hands of a clock are 4cm and 6 cm long respectively Find the sum of distance traveled by their tips in 48 hours .



Find the area of shaded region if $$AE= 9 cm$$, $$\angle AED=90^{\circ}$$, $$DE=12 cm$$.
1272612_3c18350bf99a416d9279093cb761f0e1.png



Four circles, each of radius a, touch each other. Show that area between them is $$\dfrac{6}{7}a^{2}$$.



A circle has a sector with area $$33 \pi$$ and central angle of $$\frac { 11 } { 6 } \pi$$ radius. What is the area of the circle? Either enter a exact answer in terms of $$\pi$$ or use $$\pi = 3.14$$



Rohit is going to paint the front of his house. He is not going to paint the  window and the door. If $$1\ell$$ of paint covers $$80\ m^{2}$$. How much paint will be needed the paint the front of his house?
1281172_dfa2066540424fda8d2e4442b05922e3.png



Find the perimeter and area of the shaded region in the following figure:
1282955_e41f28d4a278465390e2f8dc25d82b0d.png



The perimeter of this sector is  $$2 r + \dfrac { 7 \pi r } { 10 }$$  centimetres. Find the value of  $$x.$$
1282445_d6445e56c22f407ca15a857963e9ed35.png



Find the area of the shaded region in the given figure where $$PQRS$$ is a square of side $$12\ cm$$ and $$A,B,C$$ and $$D$$ are mi-points of the sides $$PQ, QR, RS$$ and $$PS$$.
1288528_03410cc7dc70470fab73bae30f42d240.png



Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60$$^\circ$$.



For the inauguration of an art and culture club in the school, badges were given to participants. Badges are made in the shape of an equilateral triangle of side $$6\ cm$$ with a circle of radius $$\sqrt{2}\ cm$$ inscribed in it as shown in the figure. find the area of the shaded portion 
1285397_c7fbfcec16af4716860d5a6a64df1751.png



In fig. $$15.104,$$ find the area of the shaded region (use $$\pi  = 3.14$$)
1276371_2ae321b8d0e14e2f8e1ccefcdd4f2ac9.PNG



Find the area of the shaded region.
1280317_23d5cb15fc754fe4a9815fb170834f41.png



In the figure, $$AC=24$$ cm, $$BC=10$$ and $$O$$ is the center of the circle. Find the area of shaded region.
1277769_5f92cacddb4d4d49817f67b38f80c812.png



Find the area of the shaded region given in fig.
1278092_cabb489e12c34b08b2bc830ff8a1eab9.png



A chord of a circle radius 14 cm makes a right angle at the centre . Find the area of the minor and the major segment of the circle.



Find the area of the segment of circle, given that the angle of the sector is $$120^{o}$$ and the radius and chord of the circle is $$21\ cm$$.(Take $$\pi=\dfrac{22}{7}$$)



The centre of a circle is $$C\left(1,2\right)$$ and one end of a diameter is $$A\left(3,5\right)$$, find the coordinates of the other end.



In the below sided figure, find the area of the shaded region.
1307962_6cc96882f65a4d74b11db55800c4b853.png



In the figure alongside, crescent is formed by two circles which touch at the point $$A$$. $$O$$ is the centre of the bigger circle. If radius of smaller circle is $$ = 5 \mathrm { cm }$$  and radius of larger circle is  $$ 9 \mathrm { cm },$$  find the area of the shaded region. (Take  $$\pi = 3.14$$ )
1302422_0ec73a46ca4244338aa11e8910a2931a.png



In figure, radius of circle is $$3.4\ cm$$ and perimeter of sector $$PABC$$ is $$12.8$$ cm. Find $$area( sector\ PABC)$$.
1357764_bb3a0d5e592f4b6681c5494ff2c150bb.png



Find the area of the shaded design in Fig where $$ABCD$$ is a square $$10\ cm$$ and semicircles are drawn with each side of the square as diameter. (Use $$\pi=3.14$$)
1307872_1c062f801f1a4088b7ede5e09dad101f.png



In the given figure, AOBCA represent a quadrant of area 9.625 $$\mathrm{cm^{2}}$$. Calculate the area of the shaded portion.
1315020_54b2316f210b4f4c8e13f50a8c3c3996.png



The length of an arc of a circle, subtending an angle of $$54^{\circ}$$ at the center is $$16.5\ \text{cm}$$. Calculate the radius, circumference and area of the circle.



In the given figure two concentric circle with centre $$O$$ have radii $$21cm$$ and $$42cm$$. If $$AOB=60$$ Find the area of the shaded region (Use $$\pi=\dfrac{22}{7}$$)
1399371_e7ac2be226644c54a60e753d85caba0a.png



$$AB$$ is diameter of a circle, $$CD$$ is a chord equal to the radius of the circle . Find the area of $$ABCD$$ if radius is $$\sqrt3cm$$ 



Sides of a triangular field are $$15$$ m, $$16$$ m and $$17$$ m. With the tree corners of the field a cow, a buffalo and horse are tide separately with ropes of length $$7$$ m each to graze in the field. Find the area of the field which cannot be grazed by the three animals.



Find the area of a sector, whose radius is 7 cm, with angle 72$$^0$$.



In fig. is a trapezium of area $$24.5{ cm }^{ 2 }$$ ,In it , AD||BC,$$\angle DAB={ 90 }^{ 0 }$$, AC=10 cm and BC=4 cm.If ABE is a quadrant of a circle, the area of the shaded region.
1400027_ebfca8271c714e4b947e13adc2fb4694.png



An umbrella has $$8$$ ribs which are equally spaced . Assuming umbrella to be a flat circle of radius $$45$$ cm, find the area between the two consecutive ribs of the umbrella.
1377138_3667589505a64d40a30452de7a4c4781.png



What is the area of the largest circle that can be drawn inside a square of 14 cm length.



A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diam eters which divide the circle into 10 equal sectors as shown in Fig. 12.Find :
(i) The total length of the silver wire required.
(ii) The area of each sector of the brooch.
1398137_fae2e873b8da46fca00d1f9e729bba96.png



In the figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm, to intersect the  sides BC, CA and AB at their respective mid - point D, E and F.  Find the area of the shaded region  $$(use \pi = 3.14)$$
1531784_937d40be46b64c959050af38525a153c.png



The circumference of a circle is 8 cm. Find the area of the sector whose central angle is 72$$^\circ$$.



Find the area of the shaded portion:
1511817_851c96f4eb084baab6854b8b0fb0bf22.png



Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.



In a circle of radius 12 cm., a chord subtends an angle of $${ 120 }^{ o }$$ at the centre. Find the arc of the corresponding minor segment of the circle.
1517695_1cf56bb98d94482a89ce0e6b89c9772e.png



In the given figure, OACB is a quadrant of a circle with center O and radius $$5 cm.$$ If $$OD = 2 cm$$, then find the area of the quadrant OACB.

1508359_e58e583b5780419ead6e247011b71ce1.png



Find the area of the segment of a circle of radius 12 cm whose corresponding sector has a central angle of $${ 60 }^{ \circ  }$$. 



ABC is a quadrant of circle of radius 14 cm and a semi-circle is drawn with BC as diameter. Find the area of shaded region.

1554551_d9e4ec2efc024251bb2a6b5c6838f7c6.png



In the figure, if O is the center of the circle, PQ is a chord $$\angle POQ={ 90 }^{ \circ  }$$ area of the shaded region is $$114$$ cm, Find the radius of the circle 
1508343_c28e8eeb2c0442d89f292a7457211b52.png



What is the perimeter of a square circumscribing a circle of radius $$\text{ a  cm}$$.
1593362_c81edd41c5824516870d439dc2e273f8.JPG



Fill in the blanks:
Circles having the same centre and different radii are called ______ circles.



The adjoining figure represents a rectangular lawn with a circular flower bed in the middle.
Find the area of the flower bed.
1646616_f9f37d7f060649d694dee86c7f4cb382.png



A garden is $$90\ m$$ long and $$75\ m$$ broad. A path $$5\ m$$ wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectares.



In the following figure, find the area of the shaded portion.
1646620_223365811db94b8a822eac37b28f8443.png



Find the difference of the areas of two segments of a circle formed by a chord of length 5 cm subtending an angle of $${90^ \circ }$$ at the centre.  $$\left( {\pi  = 3.14} \right)$$



Find the area of the sector of a circle of radius 5 cm, if the corresponding are length is 3.5 cm . 



In the below figure, arcs have been drawn of radius 21 cm each with vertices A,B,C and D of quadrilateral ABCD as Centers. Find the area of the shaded region.
1559718_23d5adb6c7574711a389d8fc03876da0.png



Find the area of the shaded region if $$ABCD$$ is a rectangle with sides $$8\,cm$$ and $$6\,cm$$ and $$O$$ is the center of circle.$$(Take \,\, \pi=3.14)$$
1578856_37f1a705a3c84d7888c2afd29d88177c.png



The adjoining figure represents a rectangular lawn with a circular flower bed in the middle.
Find the area of the lawn excluding the area of the flower bed.
1646617_64740d811ae6479b879539beb5a69a39.png



Split the following shapes into rectangles and find the area of each. (The measures are given in centimeters)
1675270_61eab3e95abc4c17b9caf234a89d8028.png



Find the length of an arc of a circle of radius $$14cm$$ which subtends an angle of $${36}^{o}$$ at the centre.



A piece of wire $$22$$ cm long is bent into the form of an arc of a circle subtending an angle of $$60^0$$ at its center. Find the radius of the circle $$\left[Use\,\pi=\dfrac{22}{7}\right]$$



Find the degree measure of the angle subtended at the centre of a circle of diameter $$60\ cm$$ by an arc of length $$16.5\ cm$$.



A wall is $$4.5\ m$$ long ans $$3\ m$$ high. It has two equal windows, each having forms and dimensions as shown in $$Fig. 37$$. Find the cost of painting the wall (leaving windows) at the rate of Rs $$15$$ per $$m^{2}$$.
1677177_9d385984c5bb42018bcf986215456ede.png



Find the angle in radians as well as in degrees through which a pendulum swings if its length is $$45cm$$ and its tip describes an arc of length $$11cm$$.



In a circle of diameter $$30cm$$, the length of a chord is $$15cm$$. Find the length of the minor arc of the chord.



In figure, $$\Delta ABC$$ is right angled at A. Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.
1687482_c660b9253f7b4c03baa7be30fb9d3ad5.png



Four cows are tethered at the four corners of a square field of side $$\displaystyle 50 \ m$$ such that each can graze the maximum unshared area. What area will be left ungrazed? [take $$\displaystyle  \pi = 3.14$$]



In a circle of radius $$\displaystyle 10.5 \ cm$$, the minor arc is one-fifth of the major arc. Find the area of the sector corresponding to the major arc.



A chord of a circle of radius $$\displaystyle 30 \ \text{cm}$$ makes an angle of $$\displaystyle 60^{\circ}$$ at the centre of the circle. Find the areas of the minor and major segments. [take $$\displaystyle \pi = 3.14 \ \text{and} \sqrt{3} = 1.73$$ ].



A copper wire when bent in the form of a square encloses an area of $$\displaystyle 484 \ cm^2$$. The same wire is now bent in the form of a circle. Find the area enclosed by the circle.



A horse is tethered to one corner of a field which is in the shape of an equilateral triangle of side $$\displaystyle 12 \ m$$. If the length of the rope is $$\displaystyle 7 \ m$$, find the area of the field which the horse cannot graze. [take $$\displaystyle \sqrt{3} = 1.73$$ ]. Write the answer correct to $$\displaystyle2 $$ places of decimal.



The circumference of a circle is $$\displaystyle 22 \ cm$$. Find the area of its quadrant.



A chord PQ of the circle of radius $$\displaystyle 10 \ cm$$ subtends an angle of $$\displaystyle 60$$ degrees at the centre of the circle. Find the area of minor and major segment of the circle.



A horse is placed for grazing inside a rectangular field $$\displaystyle 70 \ m $$ by $$\displaystyle 52 \ m$$. It is tethered to one corner by a rope $$\displaystyle 21 \ m $$ long. On how much area can it graze? How much area is left ungrazed?



Find the areas of both the segments of a circle of radius $$\displaystyle 42 \ cm$$ with central angle $$\displaystyle 120^0$$. [ given $$\displaystyle sin \ 120^0  = \sqrt{3}/2 \ and \ \sqrt{3} = 1.73$$ ]



The minute hand of a clock is $$\displaystyle 15 \ cm $$ long. Calculate the area swept by it in $$ \displaystyle 20 $$ minutes.



Find the area of the sector of a circle having radius $$\displaystyle 6 \ \text{cm} $$ and angle $$\displaystyle 30^{\circ}$$. [ Take $$\displaystyle \pi = 3.14$$ ]



Find the length of the arc of a circle of diameter $$\displaystyle 42 \ cm $$ which subtends an angle of $$\displaystyle 60^0$$ at the centre.



A sector of $$\displaystyle 56^0$$, cut out from a circle, contains $$\displaystyle 17.6 \ cm^2$$. Find the radius of the circle.



Find in degrees, minutes, and seconds, the dip of the horizon from the top of a mountain $$4200$$ feet high, the earth's radius being $$21 \times 10^6$$ feet.



The perimeter of a certain sector of a circle of radius $$\displaystyle 6.5 cm$$ is $$\displaystyle 31 cm$$. Find the area of the sector.



A square,whose side is $$2$$ feet, has its corners cut away so as to form a regular octagon; find its area.



In the given figure, ABCD is a square of side $$\displaystyle 4 \ cm$$. A quadrant of a circle of radius $$\displaystyle 1 \ cm$$ is drawn at each vertex of the square and a circle of diameter $$\displaystyle 2 \ cm$$ is also drawn. Find the area of the shaded region. [Use $$\displaystyle \pi = 3.14$$.]
1714463_b8f4c8cb9acf4f3a981d45756e930a0c.png



The radius of a circle is $$\displaystyle 17.5 cm$$. Find the area of the sector enclosed by two radii and an arc $$\displaystyle 44 cm$$ in length.



Given two concentric circle of radii $$r$$ and $$2r$$; two parallel tangents to the inner circle cut off an arc from the outer circle ; find its length. [Assume that $$\pi = 3.14159....,\dfrac{1}{\pi}=.31831$$ and $$\log \pi =.49715$$]



If the radius of the earth be $$4000$$ miles, find the height of balloon when the dip is $$1^o$$
Find also the dip when the balloon is $$2$$ mile high.



Find the area of a sector of a circle whose radius is $$r$$ and length of the arc is $$l$$.



Find the area enclosed by each of the following figures:

1794652_563b9bdfe5ac46c0ba5be1ed66553274.png



Three vertical post are placed are intervals of a miles along a straight canal, each rising to the same height above the surface of the waster. the visual line joining the tops of the two extreme posts cuts the middle post at a point $$8$$ inches below its top. Find the radius of the earth to the nearest milo.



Find the area of the a sector of a circle with radius $$6\ cm$$ if angle of the sector is $$60^{o}$$.



The lamn of a lighthouse is $$196$$ feet high ; how far off can be seen?



The short and long hands of a clock are $$4\ cm$$ and $$6\ cm$$ long respectively. Find the sum of distance travelled by their tips in $$2$$ days.



In Fig. sector of two concentric circles of radii $$7\ cm$$ and $$3.5\ cm$$ are shown. Find the area of the shaded region.
1785649_624e18eba2ea4cf59879767e2793c99a.png



A chord of a circle of radius $$15\ cm$$ subtends an angle of $$60^o$$ at the centre. Find the areas of  corresponding minor and major segment of the circle.(Use $$\pi=3.14$$ and $$ \sqrt 3= 1.73$$)
1785651_1dbdb37687a04a82b861187dd6b34dce.png



Find the area enclosed by the following figure:

1794651_f56c316408fe4c5ea6754407c8699db2.png



In the given figure, arcs have been drawn with radii $$14 \,cm$$ each and with centre P, Q and R. Find the area of the shaded region.
1796506_cf271cdea58645f684781f43e8d665b2.png



Find the area of a sector of a circle of radius $$28 \,cm$$ and central angle $$45^\circ.$$



In the figure, $$ A B C D $$ is a square of side $$14$$ cm. $$ A, B, C $$ and $$ D $$ are the centres of four congruent circles such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.
1803878_5832ad2e8bf64e91a71bf3f233383ebd.png



 A circle with radius $$16\,  cm$$ is cut into four equal parts and rearranged to form another shape as shown in Fig: 
Does the perimeter change? If it does change, by how much does it increase or decrease?
1794655_626d1b7c00bd454795c17272a12cf994.png



Ishika has designed a small oval racetrack for her remote control car. Her design is shown in the figure. What is the total distance around the track? Round your answer to the nearest whole cm. 
1795183_cfde2584d8a84c85af53ca692defe1d4.png



A brooch is made with silver wire in the form of a circle with is also used in making $$ 5 $$ diameters which divide the circle into  $$ 10 $$ equal sectors as shown in the figure.Find:
$$(i) $$ the total length of the silver wire required.
$$(ii)$$ the area of each sector of the brooch


1815542_4b01fae765fd4532b24173484402a7e1.PNG



A horse is tied to a pole at one corner of a square grass field of side $$ 15m $$ using $$ 10 m $$ long rope. Find 
(i) the area of that part of the field in which the horse can graze.
(ii) the decrease in the grazing area if the rope was $$ 5 m $$ long instead of $$ 10m$$.$$[Use \quad \pi=3.14]$$



A chord of a circle of radius $$ 10cm $$ subtends a right angle at the centre. Use $$ \pi =3.14 $$ and find: 
$$ (i) $$area of the minor sector 
$$(ii) $$area of the major sector



A pendulum swings through an angle $$ 60^o $$ and describes an arc $$ 8.8 cm $$ in length. Find the length of the pendulum use $$ \left[ \pi =\frac { 22 }{ 7 }  \right]  $$



A sector is cut from a circle of radius $$ 42\ \text{cm} $$. The central angle of the sector is $$ 150^\circ $$. Find the length of the arc.



In the figure (ii) given below , a square OABC is inscribed in a quadrant OPBQ of a circle . If OA= 20 cm , find the area of the shaded region .   $$ \pi =3.14 $$
1812616_e1f35ebc6c2d44faa90e62b1605026c8.png



A chord of a circle of radius $$ 12cm $$ subtends an angle of $$ 120^o $$ at the centre. Find the area of the corresponding segment of the circle $$ [Use\quad \pi =3.14, \surd 3=1.73]$$



In the given figure a square $$ OABC $$ is inscribed in a quadrant $$ OPBQ $$. If $$ OA=20 cm,$$ find the area of the shaded region.
1815629_d6af74f5decb4fdcbc700a4ad66417ea.png



$$ AB $$ and $$ CD $$ are crcs of two concentric circles of radii $$ 21 cm $$ and $$ 7 cm $$ respectively and centre $$ O $$. If $$ \angle AOB=30^o $$, find the area of the shaded region.
1815624_eca071f317c24d059dfa1112bea361d5.PNG



The minute hand of a clock is $$ 12 \space cm $$ long. Find the area of the face of the clock described by the minute hand in $$ 35 $$ minutes 



Find the angle in radian through which a pendulum swings if its length is $$75\ cm$$ the tip describes an arc of length
$$10\ cm$$



A chord PQ of a circle with a radius of 15 cm subtends an angle of $$60^\circ$$ with the center of the circle. Find the area of the minor as well as the major segment. $$(\pi = 3.14,\sqrt{3} = 1.73)$$



The minute hand of a watch is $$1.5\ cm$$ long. How far does its tip move in $$40$$ minute? (use $$\pi=3.14$$).



The length of the minute hand of a clock is $$14\ cm$$. Find the area swept by the minute hand in $$5$$ minutes.



Find the area of a quadrant of a circle whose circumference is $$22\ cm$$.



$$\Delta$$ LMN is an equilateral triangle. $$LM = 14\,cm$$. As shown in the figure, three sectors are drawn with vertices as centers and radius $$7\,cm$$.Find, Area of the shaded region.
1854305_10e4c0ed259c42e286c306ceae063725.png



In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is $$20\,cm$$. Complete the following activity to find the area of the shaded region.
1854435_cdc2ac3b30de44429f80ed1f4a3d100b.png



If in two circles, arcs of the same length subtend angles $$60^{o}$$ and $$75^{o}$$ at the centre, find the ratio of their radii.



Find the angle in radian through which a pendulum swings if its length is $$75\ cm$$ the tip describes an arc of length
$$15\ cm$$



Find the area of a sector of a circle with radius $$6\ cm$$ if angle of the sector is $$60^{o}$$.



A chord of a circle of radius $$10\ cm$$ subtends a right angle at the centre. Find the area of the corresponding:
minor segment



A horse is tied to a peg at one corner of a square grass field of side $$15\ m$$ by means of a $$5\ m$$. long rope (see Figure). Find
the area of that part of the field in which the horse can graze.
1867553_cc075096065549b0b03ad102d9afc678.png



In a circle of radius $$21\ cm$$, an arc subtends an angle of $$60^{o}$$ at the Centre. Find:
area of the segment formed by the corresponding chord.



A chord of a circle of radius $$10\ cm$$ subtends a right angle at the centre. Find the area of the corresponding:
major sector. (Use $$\pi=3.14$$)



In a circle of radius $$21\ cm$$, an arc subtends an angle of $$60^{o}$$ at the Centre. Find:
the length of the arc.



A chord of a circle of radius $$15\ cm$$ subtends an angle of $$60^{o}$$ at the centre. Find the area of the corresponding minor and major segments of the circle.
(Use $$\pi=3.14$$ and $$\sqrt{3}=1.73$$).



In a circle of radius $$21\ cm$$, an arc subtends an angle of $$60^{o}$$ at the Centre. Find:
area of the sector formed by the arc.



An umbrella has $$8$$ ribs which are equally spaced (see the figure). Assuming umbrella to be a flat circle radius $$45\ cm$$, find the area between the two consecutive ribs of the umbrella.
1867580_37ebc019e23948dd91a3ba1c73066a32.png



A horse is tied to a peg at one corner of a square grass field of side $$15\ m$$ by means of a $$5\ m$$. long rope (see Figure). Find
the increase in the grazing area if the rope were $$10\ m$$ long instead of $$5\ m$$. (use $$\pi=3.14$$)
1867557_73227515517340f8ab13c55c3181d9ae.png



A brooch is made with silver wire in the form of a circle with diameter $$35\ mm$$. The wire is also used in making $$5$$ diameter which divide the circle into $$10$$ equal sectors as shown in the Figure.
Find
the area of each sector of the brooch.
1867570_71669173a2854c24970afddd31686576.png



In the given figure, $$OACB$$ is a quadrant of a circle with center $$O$$ and radius $$3.5\ cm$$. If $$OD=2\ cm$$, find the area of the 
Quadrant $$OACB$$



The minute hand of a clock is $$10cm$$ long Find the area  of the face of the clock described by the minute hand between $$10\ AM$$ and  $$10-30\ AM$$



An arc of circle of radius $$21\,cm$$, subtends an angle $$60^\circ$$ at the center, then find the area of the corresponding major sector.



Radius of a circle is $$7\,cm$$ and angle subtended at the center is $$60^\circ$$. Find the length of the arc.



In a circle of diameter $$40 cm$$, the length of a chord is $$20 cm$$. Find the length of minor arc of corresponding chord.



A car has two wipers which do not overlap. Each wiper has a blade of length $$25\ cm$$ sweeping through an angle of $$115^{o}$$. Find the total area cleaned at each sweep of the blades.



In the given figure, $$OACB$$ is a quadrant of a circle with center $$O$$ and radius $$3.5\ cm$$. If $$OD=2\ cm$$, find the area of the 
Shaded region.



If in two circles, arcs of the same length subtend angles of $$60^{0}$$ and $$75^{0}$$ at the centre, find the ratio of their radii.



How much time the minute hand of a watch will take to describe an angle of $$120^{\circ} $$ ?



Find the length of the arc that subtends an angle of $$72^o$$ at the centre of a circle of radius $$5cm$$.



The diagram shows two arcs, A and B. Arc A is part of the circle with centre O and radius OP. Arc B is part of the circle with centre M and radius PM, where M is the mid - point of PQ. Show that the area enclosed by the two arcs is equal to 25$$\left ( \sqrt{3} \, - \, \dfrac{\pi}{6} \right )cm^2$$



Find the area of the shaded portion from the given figure.
698872_d9220edc23884f339aca6638bde62502.png



Find the area of the segment $$AYB$$ show in the figure, if radius of the circle is $$21cm$$ and $$\angle{AOB}=120^{\circ}$$(Use $$n=\dfrac {22}{7})$$
1062587_e726de26e4484293a4084fe2105a39fc.PNG



An equilateral $$\triangle$$ of side $$6\ cm$$ is inscribed in a $$\odot $$. Find area of region extension to $$\triangle$$ to and within the $$\odot $$.



A chord of a circle of radius $$12\ cm$$ subtends an angle of$$120^{\circ}$$ at the centre. Find the area of the corresponding segment of the circle.
$$\left [ take\pi =3.14and\sqrt{3}=1.73 \right ]$$



Find the area of the shaded portion
1326109_e2a604d82cb7466b91d80b0e426976a7.png



Find area of the following polygons:
1114261_8b5d0aa5835c4a5eaebf480b13a2c0d7.JPG



Find the lengths of the arcs cut off from a circle of radius $$12$$ $$cm$$ by a chord $$12$$ $$cm$$ long. Also, find the area of the minor segment.
$$[ Take \pi = 3.14 \text { and } \sqrt { 3 } = 1.73 . ]$$



Find the perimeter and the area of the shaded region in the following figures. All measurements all in centimetres. 
1409090_8e70cbff55034fbda7a8243a826fdfe8.png



Three horse are tethered at $$3$$ corners of a triangular plot having sides $$20\ m,30\ m$$ and $$40\ m$$ with ropes of $$7\ m$$ length each. Find the area of this plot which can be grazed by the horses.



Radha made a picture of an aeroplane with coloured paper as shown in Fig $$12.15 $$. Find the total area of the paper used.
1246881_44b735a6762449cd8621764c41ce24ee.jpg



The radius of a circle is $$9\ cms$$. Find the length of an arc of this circle which cuts off a chord of length equal to length of radius.



In the figure (i) given below , OBC is a quadrant of a circle . The radius OA = .5 cm  and OD = 2cm. Calculate the area of the shaded portion .
1812541_4a92294bd22840acaf469822831f5d12.png



The quadrant show in the figure (ii) given below are each of radius 7 cm. Calculate the area of the shaded portion . 
1812601_04e1f492e9c8440c801ef1a5af3e7c08.png



The diameter of a circle is $$10$$ feet; find the area of a sector whose arc is $$22\dfrac{1}{2}^o$$.[Assume that $$\pi = 3.14159....,\dfrac{1}{\pi}=.31831$$ and $$\log \pi =.49715$$]



In the given figure, $$O$$ is the centre of the circle, $$BO$$ is the bisector of $$\angle ABC$$. Show that $$AB=AC$$.
1670558_b5d621adeacb491faf31d69949bb96e6.png



In the figure given below, a chord AB of a circle of radius 10 cm subtends a right angle the center ) Find the are of the sector OACB and pf the major segment.Take $$\pi  = 3.14$$.



The measure of an arc of a circle is $$60^o$$ and its radius is $$15cm$$. Find the length of the arc. $$(\pi=3.14)$$



Find the length of a chord which is at a distance of $$5\ cm$$ from the centre of a circle of radius $$10\ cm$$.



Class 10 Maths Extra Questions