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CBSE Questions for Class 7 Maths Perimeter And Area Quiz 12 - MCQExams.com
CBSE
Class 7 Maths
Perimeter And Area
Quiz 12
A rectangle has an area $$304$$ square hectares. Find its area in meters.
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$$3,040$$ $$m^2$$
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$$30,400$$ $$m^2$$
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$$3,04,000$$ $$m^2$$
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$$3,040,000$$ $$m^2$$
A tire on a car rotates at 500 RPM (revolutions per minute) when the car is traveling at 50 km/hr (kilometers per hour). What is the circumference of the tire, in meters?
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$$10\pi/6$$
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$$50,000/(60*2\pi)$$
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$$50,000/(500*2\pi)$$
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$$10/6$$
Explanation
Speed $$=50km/hr=50,000m/hr$$
speed $$(in \, m/min)=50,000/60\,m/min$$
In any given minute the car travels $$50,000/60m/min$$ and tire volutes $$500$$ times around or $$500$$ time its circumference.
Let the circumference be C.
$$\Rightarrow 50,000/60=500C$$
$$C=\dfrac{50,000}{500\times 60}$$
$$C=\dfrac{10}{6}m$$
The area of the given figure ABCDEF is
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$$22.82$$ $$\displaystyle cm^{2}$$
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$$25.82$$ $$\displaystyle cm^{2}$$
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$$26.82$$ $$\displaystyle cm^{2}$$
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$$28.82$$ $$\displaystyle cm^{2}$$
In the given figure, what is the area of $$\triangle PQR
$$?
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$$15\sqrt{3}\: cm^2$$
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$$27\sqrt{5}\: cm^2$$
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$$3\sqrt{15}\: cm^2$$
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$$45\sqrt{3}\: cm^2$$
The length of a rectangle is twice the diameter of a circle. The circumference of the circle is equal to the area of a square of side 22 cm. What is the breadth of the rectangle, if its perimeter is 668 cm?
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$$24 \ cm$$
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$$26 \ cm$$
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$$52 \ cm$$
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Cannot be determined
Explanation
Given that, circumference of the circle is equal to the area of a square of side $$ 22 \ cm $$.
We know that, circumference of a circle is $$2\pi r$$
and area of a square is $$side\times side$$
$$\therefore \ 2\pi r = side \times side $$
$$\Rightarrow 2 \times \cfrac {22}{7} \times radius = 22 \times 22 \quad \quad [\because \ \pi=\frac{22}{7}]$$
$$\Rightarrow$$ radius $$(r)= 77 \ cm $$
Given that, the length of a rectangle is twice the diameter of a circle.
$$\Rightarrow$$ length $$= 2(77 \times 2) = 308 \ cm \quad \quad [\because d=2r]$$
Also given that, the perimeter of the rectangle is $$ 668 \ cm $$.
$$\therefore \ 2(length + breadth ) = 668 $$
$$\Rightarrow length + breadth = 334 \ cm $$
$$\Rightarrow 308 + breadth = 334 \quad \quad [\because length=308\ cm]$$
$$\Rightarrow$$ breadth $$= 26 \ cm $$
Hence, the breadth of the rectangle is $$26\ cm$$.
If one leg of an isosceles right-angled triangle is increased by $$6$$ cm and that of the other leg decreased by $$4$$ cm, then the area of the triangle decreases by $$24$$ sq cm. Find the length of the leg of the original triangle
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$$36$$ cm
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$$30$$ cm
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$$24$$ cm
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none of these
The outer circle has center $$O$$ and circumference $$p$$. $$OT$$ is a diameter of the inner circle.
The circumference of the inner circle
$$\dfrac {1}{2}p$$
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If the quantity in Column A is greater
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If the quantity in Column B is greater
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If the two quantities are equal
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If the relationship cannot be determined from the information given
Explanation
Let the radius of outer circle be $$r$$.
Circumference $$p$$ of outer circle is $$2 \times \pi \times r $$
$$ i.e. p = 2 \pi r$$.
Now the radius of inner circle is $$\dfrac {r}{2}$$, so the circumference of innercircle is $$2 \times \pi \times \dfrac {r}{2} = \pi \times r = \dfrac {p}{2}$$.
Therefore, the quantities in two columns are equal.
So, the correct option is $$C$$.
Find the area of the shaded region in the following figure
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28. 45 sq. cm
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113.6 sq. cm
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59.8 sq. cm
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46.88 sq. cm
In the figure above, the four circles have the same center and their radii are $$1, 2, 3$$ and $$4$$, respectively. What is the ratio of the area of the small shaded ring to the area of the large shaded ring?
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$$1 : 2$$
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$$1 : 4$$
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$$3 : 5$$
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$$3 : 7$$
Explanation
We know that
area of circle is $$ \pi \times {r}^{2}$$, where $$r$$ is radius.
Area of small shaded ring is $$ \pi \times ({ 2 }^{ 2 }-{ 1 }^{ 2 }) = \pi \times 3$$.
Area of large shaded region is $$ \pi \times ({ 4 }^{ 2 }-{ 3 }^{ 2 }) = \pi \times 7$$.
The ratio of smaller to larger shaded regions is $$ \pi \times \dfrac {3}{\pi }\times 7 = \dfrac {3}{7}$$.
ABCD is a parallelogram, E is the mid-point of AB and CE bisects $$\displaystyle \angle BCD$$, the $$\displaystyle \angle DEC$$ is:
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$$\displaystyle { 60 }^{ \circ }$$
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$$\displaystyle { 90 }^{ \circ }$$
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$$\displaystyle { 100 }^{ \circ }$$
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$$\displaystyle { 120 }^{ \circ }$$
Circle $$C_1$$ passes through the centre of circle $$C_2$$ and is tangential to it. If the area of $$C_1$$ is $$4cm^2$$, then the area of $$C_2$$ is ________.
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$$8cm^2$$
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$$8\sqrt{\pi}cm^2$$
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$$16cm^2$$
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$$16\sqrt{\pi}cm^2$$
If it costs Rs.$$320$$ to carpet a square room $$8$$ metres broad, what would it cost, at the same rate per square metre, to carpet an oblong room $$6$$ metres by $$5$$ metres?
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Rs.$$160$$
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Rs.$$250$$
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Rs.$$150$$
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Rs.$$320$$
A hectare of land is divided into plots each $$25$$ metres long and $$20$$ metres broad. How many plots are there?
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$$20$$
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$$50$$
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$$40$$
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$$25$$
A rectangular garden 63 m long and 54 m board has a path 3 m wide inside it. Find the cost of paving the path at Rs, 37/2 per square meter :
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Rs. 12321
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Rs. 11100
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Rs. 74000
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none of these
A parallelogram has sides 30 cm and 20 cm and one of its diagonal is 40 cm long. Then its area is:
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$$75\sqrt { 5 } { cm }^{ 2 }$$
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$$245\quad { cm }^{ 2 }$$
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$$150\sqrt { 15 } { cm }^{ 2 }$$
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$$300\quad { cm }^{ 2 }$$
The mid points of the sides of a parallelogram are joined to form a small parallelogram. it the area of the small parallelogram is 20sq.cm then the area of the original parallelogram is
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30 sq.cm
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40 sq.cm
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45 sq.cm
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80 sq.cm
What is the minimum radius (>1) of a circle whose circumference is an integer ?
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2
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$$\dfrac { 4 }{ \pi } $$
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$$\dfrac { 6 }{ \pi } $$
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$$\dfrac { 3 }{ \pi } $$
Length of chord $$AB=14\sqrt{2}$$ and $$\angle{ACB}=45^{\circ}$$ in the adjoining figure of a circle with centre 'O'. Find the area of this circle.
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308 $$cm^2$$
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154 $$cm^2$$
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2464 $$cm^2$$
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616 $$cm^2$$
find the diameterof the circle given the area
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$${ 616m }^{ 2 }$$
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$${ 1386m }^{ 2 }$$
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$${ 2464m }^{ 2 }$$
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$${ 55.44m }^{ 2 }$$
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