Mathematics · Quantitative Aptitude

Circle Geometry

232 Questions

Circle geometry focuses on the properties and dimensions of circles, including radius, diameter, circumference, and area calculations. Questions often involve concentric circles, sectors, and inscribed shapes. This topic frequently appears in quantitative aptitude sections of major competitive exams.

Area and circumferenceConcentric circlesCircle sectorsInscribed polygonsSemicircle area

Circle Geometry Questions

Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments
The radius of a circle is $7 cm$, then area of the sector of this circle if the corresponding angle is $30^{\circ}$ is 
  1. $12.83 \,cm^2$
  2. $11.83 \,cm^2$
  3. $12.25 \,cm^2$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of a sector of a circle of radius '$r$' and angle $ = \dfrac { \theta  }{ 360 } \pi {r}^{2}$
Hence, area of the sector of the circle of  radius $ 7 $ cm and angle $ = \dfrac { 30 }{ 360 } \times \dfrac { 22 }{ 7 } \times 7 \times 7 = 12.83 \ \text{cm}^{2} $

Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

The radius of a circle is $7 cm$, then area of the sector of this circle if the corresponding angle is:$210^{\circ}$ is 

  1. $88.83 \,cm^2$
  2. $87.83 \,cm^2$
  3. $89.83 \,cm^2$
  4. $86.83 \,cm^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area of a sector of a circle of radius 'r' and angle  $ \theta = \dfrac { \theta  }{ 360 } \pi {r}^{2}$

Hence,area of the sector of the circle of  radius $ 7 $ cm and angle $ { 210 }^{

0 } = \dfrac { 210 }{ 360 } \times \dfrac { 22 }{ 7 } \times 7 \times

7\quad = 89.83  {cm}^{2} $


Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

The area of a circle is 314 sq. cm and area of its minor sector is 31.4 sq. cm. Find the area of its major sector.

  1. 282.6c$m^2$
  2. 200.6c$m^2$
  3. 180.04c$m^2$
  4. 1220.09c$m^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given:
Area of circle = $314 $$cm^2$
Area of minor sector = $31.4 $$cm^2$
Area of major sector = Area of a circle - Area of minor sector
= $314 - 31.4 cm^2$
= $282.6$ $cm^2$

Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

The radius of a circle is $3.5$ cm and area of the sector is $3.85$ $cm^2$. Find the length of the corresponding arc.

  1. $2.2cm$
  2. $4.2cm$
  3. $5.1cm$
  4. $6.2cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the angle of centre made by the sector be $\theta$
Therefore,
Area of the sector=$\pi r^2\dfrac{\theta }{360}$
                        $=>3.85=\dfrac{\pi(3.5)^2\theta}{360}$


                        $=>\theta=\dfrac{3.8\times 360\times 7}{(3.5)^2\times 22}$
                        $=35.5$
                        $=36$
Thus length of the arc =$2\pi r\dfrac{\theta}{360}$
                                   =$2\times \dfrac{22}{7}\times 3.5\times \dfrac{36}{360}$
                                   =$2.2cm$

Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

The area of the sector of a circle whose radius is 6 m when the angle at the centre is $\displaystyle 42^{\circ}$ is 

  1. $\displaystyle 13.2\:m^{2}$
  2. $\displaystyle 14.2\:m^{2}$
  3. $\displaystyle 13.4\:m^{2}$
  4. $\displaystyle 14.4\:m^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of sector $\displaystyle =\frac{42}{360}\times \pi r^{2}$
$\displaystyle =\frac{42}{360}\times \frac{22}{7}\times6\times6=13.2m^{2}$

Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

A sector of $120^{\circ}$ cut out from a circle has an area of $9\displaystyle \frac {3}{7}$ sq cm. The radius of the circle is

  1. $3$ cm
  2. $2.5$ cm
  3. $3.5$ cm
  4. $3.6$ cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, area of an sector $=9\dfrac {3}{7}$ sq. cm , $\theta=120^0$
We know Area of sector $=\dfrac {\theta}{360}\times \pi r^2$
$\Rightarrow \displaystyle \frac {\theta}{360}\, \times\, \pi r^2\, =\, 9\, \displaystyle \frac {3}{7}$
$\Rightarrow \displaystyle \frac {120}{360}\, \times\, \displaystyle \frac {22}{7}\, \times\, r^2\, =\, \displaystyle \frac {66}{7}$
$\Rightarrow r^2\, =\, \displaystyle \frac {66}{7}\, \times\, \displaystyle \frac {360}{120}\, \times\, \displaystyle \frac {7}{22}\, =\, 9$
$\Rightarrow r\, =\, \sqrt 9\, =\, 3$ cm

Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

The area of the sector of a circle, whose radius is $6$ m when the angle at the centre is $42^0$, is

  1. $13.2$ sq. m
  2. $14.2$ sq. m
  3. $13.4$ sq.m
  4. $14.4$ sq. m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given, $\theta=42^0$, radius $=6$ m
Area of sector $=\, \displaystyle \frac {\theta}{360}\, \times\, \pi r^2$
$=\displaystyle \frac {42}{360}\, \times\, \displaystyle \frac {22}{7}\, \times\, 6\, \times\,6$
$ =\, 13.2$ sq. m
Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

A sector of $120^{\circ}$ cut out from a circle has an area of $9\displaystyle \frac{3}{7}$sq cm. The radius of the circle is

  1. $3 cm$
  2. $2.5 cm$
  3. $3.5 cm$
  4. $3.6 cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Let radius of circle be $'r' cm$. Then,
$\cfrac { \theta  }{ 360° } \times \pi { r }^{ 2 }=9\cfrac { 3 }{ 7 } cm^2=\cfrac { 66 }{ 7 } cm^2$
$\Rightarrow \cfrac { 120° }{ 360° } \times \cfrac { 22 }{ 7 } \times { r }^{ 2 }=\cfrac { 66 }{ 7 } \Rightarrow { r }^{ 2 }=\cfrac { 66\times 7\times 360° }{ 120°\times 22\times 7 } =9$
$\Rightarrow r=\sqrt { 9 } =3 cm$
Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

The area of a sector with  perimeter as  $45\ cm$ and radius as $6 \ cm$ is

  1. $44$ $ \displaystyle cm^{2} $
  2. $66$ $ \displaystyle cm^{2} $
  3. $88$ $ \displaystyle cm^{2} $
  4. $99$ $ \displaystyle cm^{2} $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\Rightarrow$  Perimeter of a sector $=45\,cm$


$\Rightarrow$  Radius of a circle $(r)=6\,cm$


$\Rightarrow$  Arc of sector $(l)=Perimeter\,of\,sector-2r$
                             $=45-(2\times r)$
                             $=45-(2\times 6)$
                             $=45-12$
                             $=33\,cm$

$\Rightarrow$  Area of sector $=\dfrac{1}{2}\times r\times  l\\$
                               $=\dfrac{1}{2}\times 6\times 33\\$
                               $=3\times 33$
                               $=99\,cm^2$

Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

Find the area of a sector with an arc length of $20 cm$ and a radius of $6 cm$.

  1. $20$ $cm^2$
  2. $40$ $cm^2$
  3. $60$ $cm^2$
  4. $80$ $cm^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area of sector $=$ $\dfrac { Arc.length }{ 2\pi r } \times \pi { r }^{ 2 }$


                         $=$ $\dfrac { 20 }{ 2\pi r } \times \pi \times 6\times 6=60{ cm }^{ 2 }$

Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

The area of a sector with a radius of $2 cm$ is $12 $$cm^2$. Calculate the angle of the sector. 

(Assume $\pi = 3$)

  1. $360^o$
  2. $160^o$
  3. $90^o$
  4. $180^o$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$r = 2$cm
$A = 12cm^2$
Area of sector $=\dfrac {\theta}{360} \times \pi r^2$

$12 = \dfrac {\theta}{360} \times 3 \times 2^2$

$\theta = \dfrac {12 \times 360}{3 \times 4}$

$\theta = 360^o$