MCQ Questions for Class 10 Maths Areas Related To Cricles Quiz 5

The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal ? Why ?

0%
True
0%
False

Explanation

Using usual abbreviations for sectors

$A_1 = A_2$ [Given]

$\Rightarrow \dfrac{\pi r^2_1 \theta_1}{360^\circ} = \dfrac{\pi r^2_2 \theta_2}{360^\circ}$

$\Rightarrow r^2_1 \theta_1 = r^2_2\theta_2$

$\Rightarrow \dfrac{\theta_1}{\theta_2} = \dfrac{r^2_2}{r^2_1}$

Now, $\dfrac{l_1}{l_2} = \dfrac{2\pi r_1\theta_1}{2\pi r_2\theta_2} = \dfrac{r_1}{r_2} \times \dfrac{r^2_2}{r^2_1} = \dfrac{r_2}{r_1}$

$\Rightarrow \dfrac{l_1}{l_2} = \dfrac{r_2}{r_1}$

Hence, arcs length can be equal if $\dfrac{r_2}{r_1} = 1$ i.e., $r_1 = r_2 = r.$

Hence, the given statement is false.

Is the area of circle inscribed in a square of side

$a \,cm, \pi a^2 \,cm^2 ?$ Give reasons for your answer.

0%
True
0%
False

Explanation

The radius of the circle inscribed in a square of side

$a$ cm is

$r = \dfrac{a}{2}$

$\therefore$ Area of circle

$= \pi r^2$

$= \pi \left ( \dfrac{a}{2} \right )^2 = \dfrac{\pi a^2}{4} \,cm^2$

$\neq \pi a^2 \,cm^2$
Hence, the given statement is false.
1763541_1796427_ans_f1f432f46a3f4dbab5cf37b525ad8136.png

The area of two sectors of two different circles with equal corresponding arc length are equal. Is this statement true ? Why ?

0%
True
0%
False

Explanation

Consider two circles of radii

$r_1, r_2$ or arc length

$l_1$ and

$l_2$ and their corresponding angles of sectors

$\theta_1, \theta_2$ in degrees respectively.

$l_1 = r_1\theta_1\dfrac{\pi}{180^\circ}, l_ 2= r_2\theta_2\dfrac{\pi}{180^\circ}$
Now,

$l_1 = l_2$ [Given]

$\Rightarrow r_1\theta_1 = r_2\theta_2 = x$ [say]
Area of sector

$A_1$ and

$A_2$ are given by

$A_1 = \dfrac{\pi r^2_1 \theta_1}{360^\circ}, A_2 = \dfrac{\pi r^2_2 \theta_2}{360^\circ}$

$\therefore \dfrac{A_1}{A_2} = \dfrac{\dfrac{\pi r_1\theta_1r_1}{360^\circ}}{\dfrac{\pi r_2\theta_2r_2}{360^\circ}} = \dfrac{xr_1}{xr_2} = \dfrac{r_1}{r_2}$

$\Rightarrow \dfrac{A_1}{A_2} = \dfrac{r_1}{r_2}$
Area of sector can be equal when

$\dfrac{r_1}{r_2} = 1 i.e.,$ equal radii. So, the areas of sectors of two circles of same arcs lengths are not equal.
Hence, the given statement is false.

If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius

$2r,$ then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of other circle. Is this statement false ? Why ?

0%
True
0%
False

Explanation

Consider two circles

$C_1$ and

$C_2$ of radii r and 2r respectively.
Let the length of two arcs be

$l_1$ and

$l_2.$

$l_1 = \widehat{AB}$ of

$C_1 = \dfrac{2\pi r \theta_1}{360^\circ}$

$l_2 = \widehat{CD}$ of

$C_2 = \dfrac{2\pi r \theta_2}{360^\circ} = \dfrac{2\pi . 2r \theta_2}{360^\circ}$
According

$l_1 = l_2$

$\Rightarrow \dfrac{2\pi r \theta_1}{360^\circ} = \dfrac{2\pi.2r \theta_2}{360^\circ}$

$\Rightarrow \theta_1 = 2\theta_2$
i.e., Angle of sector of the 1st circle is twice the angle of the sector of the other circle.
Hence, the given statement is true.

The center of the circle lies

0%
in the interior of the circle
0%
in the exterior of the circle
0%
on the circle
0%
None of these

The shaded portion of the circle represents

0%
Semicircle
0%
Diameter
0%
A sector of the circle
0%
Segment

A chord divides a circle into two

0%
Diameter
0%
Semicircle
0%
Sectors
0%
Segments

In the given figure,

$r$ represents

0%
Radius
0%
Diameter
0%
Tangent
0%
Chord

Explanation

${\textbf{Step -1: Find r.}}$

${\text{The distance from the center point to any point on the circle is called the radius of a circle}}$

${\text{Here, r is the radius in the figure.}}$

${\textbf{Hence, the correct answer is option A.}}$

In the adjoining figure,

$18 in$ is the length of

0%
Radius
0%
Diameter
0%
Any chord other than the diameter
0%
None of these

An arc is a part of a circle.

0%
True
0%
False

In the figure given above, radius of a greater circle is

$r\ cm$ . Find the area of non-shaded portion

0%
$\dfrac {9\pi r^{2}}{16} sq. cm$
0%
$\dfrac {3\pi r^{2}}{4} sq. cm$
0%
$2\pi r^{2} sq. cm$
0%
$\dfrac {4\pi r^{2}}{3} sq. cm$

Explanation

Radius of big semicircle

$=r$

Area of big semicircle

$=\cfrac {\pi r^2}{2}$

Radius of small semicircles

$=r/2$

Area of smaller semicircle

$= \cfrac 12 \times \cfrac {\pi r^2}{4}$

Area of 2 smaller semicircles

$= \cfrac {\pi r^2}{4}$

Area of non-shaded region

$=$ Area of big semicircle

$+ 2 \times$ Area of the smaller semicircles

Area of non-shaded region

$=\cfrac {\pi r^2}{2} + \cfrac {\pi r^2}{4}= \cfrac {3 \pi r^2}{4}$

Find the area of sector when its area is

$6cm$ and radius

$5cm$

0%
$15$ sq.cm
0%
$25$ sq.cm
0%
$18$ sq.cm
0%
$27$ sq.cm
0%
$72$ sq.cm

The radius of a circle is

$14$ metres. A chord of this circle subtends an angle of

${60}^{o}$ at the centre. Find the area of the smaller segment cur off by the chord.

0%
$196\left( \cfrac { \pi }{ 6 } +\cfrac { \sqrt { 3 } }{ 4 } \right)$
0%
$196\left( \cfrac { \sqrt { 3 } }{ 4 } -\cfrac { \pi }{ 6 } \right)$
0%
$196\left( \cfrac { \pi }{ 6 } -\cfrac { \sqrt { 3 } }{ 4 } \right)$
0%
$196\left( \cfrac { \pi }{ 2 } -\cfrac { \sqrt { 3 } }{ 4 } \right)$
0%
NONE OF THESE

A horse is tied to a pole fixed at one corner of a

$50m\times 50$ square field of grass of means of a

$20m$ long rope. What is the area of that part of the field which the horse can gaze?

0%
$1256{m}^{2}$
0%
$942{m}^{2}$
0%
$628{m}^{2}$
0%
$314{m}^{2}$

A rope by which a calf is tied is increased by

$12m$ to

$23m$ . How much additional grassy ground shall it graze?

0%
$1020{m}^{2}$
0%
$1120{m}^{2}$
0%
$1210{m}^{2}$
0%
$1021{m}^{2}$

A rope by which a calf is tied is increased from

$12m$ to

$23m$ . How much additional grassy ground shall it graze?

0%
$1200{m}^{2}$
0%
$1250{m}^{2}$
0%
$1210{m}^{2}$
0%
$1225{m}^{2}$

If the radius of a circle and the central angle are 21 cm and

$60^\circ$ respectively, then the length of the arc is __________.

0%
20 cm
0%
21 cm
0%
22 cm
0%
24 cm

The area of minor sector of

$\odot$ (0,10)isThe length of its corresponding arc is-----.

0%
15
0%
90
0%
60
0%
30

CBSE Questions for Class 10 Maths Areas Related To Cricles Quiz 5 - MCQExams.com

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Practice Class 10 Maths Quiz Questions and Answers

CBSE Questions for Class 10 Maths Areas Related To Cricles Quiz 5 - MCQExams.com

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Practice Class 10 Maths Quiz Questions and Answers

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