Mathematics · Quantitative Aptitude

Circle Geometry

250 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 between two concentric circles the area of ring semicircle and ring

A circular park has a path of uniform width around it. The difference between outer and inner circumference of the circular path is $132\ m$. Its width is _____ $\displaystyle \left(\pi=\frac{22}{7}\right)$

  1. $22\ m$
  2. $20\ m$
  3. $21\ m$
  4. $24\ m$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given $\displaystyle 2\pi r _{2}-2\pi r _{1}=132$
$\displaystyle \Rightarrow r _{2}-r _{1}=\frac{132}{2\pi }=\frac{132\times 7}{44}=21\ m$

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The inner circumference of a circular track $14\ m$ wide is $440\ m$. The radius of the outer circle is

  1. $70\ m$
  2. $56\ m$
  3. $77\ m$
  4. $84\ m$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Inner circumference $= \displaystyle 2\pi r=2\times \frac{22}{7}\times r=\frac{44r}{7}$
Given $\displaystyle \frac{44r}{7}=440\Rightarrow r=\frac{440\times 7}{44}=70\ m$
$\displaystyle \therefore $ Radius of outer circle $= 70\ m + 14\ m = 84\ m$ 

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

If the perimeter of a semi-circle is $36\ cm$. What will be its diameter?

  1. $88\ cm$
  2. $22\ cm$
  3. $28\ cm$
  4. $14\ cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Perimeter of semicircle$=36cm$
$\pi r+d=36$
$\Rightarrow \pi r+2r=36$
$\Rightarrow r\left( \cfrac { 22 }{ 7 } +2 \right) =36$
$\Rightarrow \cfrac { 36 }{ 7 } \times r=36$
$\Rightarrow r=7$
$\therefore $ Diameter $2r=2\times 7=14cm$
Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

If a wire is bent into the shape of a square the area of the square is 81 sq cm .When the wire is bent into a semi circular shape; what is the area of the semicircle? $\displaystyle \left ( \pi =\frac{22}{7} \right )$

  1. $\displaystyle 77\:\text{cm}^{2}$
  2. $\displaystyle 73\:\text{cm}^{2}$
  3. $\displaystyle 37\:\text{cm}^{2}$
  4. $\displaystyle 33\ \text{cm}^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let '$a$' be the length of each side of the square
Then $\displaystyle a^{2}=81\Rightarrow a=9$ cm
Length of wire $=$ Perimeter of square
=$ 4a= 36$ cm
$\displaystyle \Rightarrow $ Circuference of semicircle $= 36$ cm
$\displaystyle \Rightarrow \pi r+2r=36$

$ \displaystyle \Rightarrow r\left ( \pi +2 \right )=36$
$\displaystyle \Rightarrow  r =\dfrac{36}{\pi +2}=\dfrac{36}{\dfrac{22}{7}+2}=\dfrac{36\times 7}{\left ( 22+14 \right )}=\dfrac{36\times 7}{36}$ cm $=7$ cm
$\displaystyle \therefore \ \text{Area of the semicircle}=\frac{1}{2}\pi r^{2}$
$\displaystyle =\dfrac{1}{2}\times \dfrac{22}{7}\times 7\times \text{cm}^{2}=77\text{cm}^{2}$

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

If the radii of two concentric circles are $15\ cm$ and $13\ cm$ respectively then the area of the circulating ring in sq cm will be

  1. $176$
  2. $178$
  3. $180$
  4. $200$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$R = 15\ cm, r = 13\ cm$
Area of the circulating ring 
$\displaystyle = \pi \left(R^2-r^2\right)$

$\displaystyle =\pi \left ( R+r \right )\left ( R-r \right )$
$\displaystyle =\frac{22}{7}\left ( 15+13 \right )\times \left ( 15-13 \right )$
$\displaystyle \frac{22}{7}\times 28\times2$
$= 176$ sq cm

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

If a wire is bent into the shape of a square, then the area of the square is $81\ cm^{2}$. When the same wire is bent into a semi-circular shape, then the area of the semi circle will be

  1. $22\ cm^{2}$
  2. $44\ cm^{2}$
  3. $77\ cm^{2}$
  4. $154\ cm^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the side of the square be $a$ cm

Thus, perimeter is $4a$ and area of the square is $a^2$
$\therefore a^2=81$
$\Rightarrow a=\sqrt{81}$
$\Rightarrow a=9$
Thus, perimeter $=4 \times 9$ $=36$ cm
Now, wire is bent into a semicircle.
Therefore, $2r+πr=36$
$⇒r(π+2)=36$ $
$⇒r=\cfrac{36}{\dfrac{22}{7}+2}$

$⇒r=\cfrac { 36 }{\dfrac{36}{7}}$
$⇒r=7$ cm

Area of semicircle $=\cfrac{1}{2}πr^2$
$=\cfrac{1}{2}×\cfrac{22}{7}×7×7$
$=77\ cm^2$

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The areas of two concentric circles forming a ring are 154 sq cm and 616 sq cm The breadth of the ring is

  1. $21 cm$
  2. $56 cm$
  3. $14 cm$
  4. $7 cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Breadth of the ring is equal to the difference between the radius of the outer circle and the radius of the inner circle
Given the area of outer circle=616$\displaystyle cm^{2}$
$\displaystyle \Rightarrow  \pi r _{2}^{2}=616 cm^{2}$
$\displaystyle \Rightarrow r _{1}^{2}=\frac{616\times 7}{22}=196$
$\displaystyle \therefore r _{1}=14 cm $
and the area of the inner circle $\displaystyle =154 cm^{2}$
$\displaystyle \Rightarrow \pi r _{2}^{2}= 154$
$\displaystyle \Rightarrow r _{2}^{2}=\frac{154\times 7}{22}=49$
$\displaystyle \therefore r _{2}=7 cm.$
$\displaystyle \therefore $ The required answer $\displaystyle =r _{1}-r _{2}=14-7=7 cm.$

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

If the difference between the circumference and radius of a circle is 37 cm, then the area of the circle is

  1. $111 cm^2$
  2. $148 cm^2$
  3. $259 cm^2$
  4. $154 cm^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Consider the difference between circumference and radius.


Taking$\pi $ as $3.14$ will give an approximate answer. we can do it by taking $22/7$ as wel


Let, the radius be$ r cm$


Circumference will be,

$2r=2\times 3.14r=6.28r$


ATQ,  $6.28r-1.r=37$

$5.28r=37$

 $r=\dfrac{37}{5.28}$

$r=$approx. $7 cm$ 

Area$=\pi {{r}^{2}}=3.14\times 7\times 7=154c{{m}^{2}}$


Hence, this is the answer.

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

If the circumference of a circle is reduced by 50%, then the area will be reduced by

  1. 50%

  2. 25%

  3. 75%

  4. 12.5%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let the original radius be $r$.
So, the area of circle $=\pi r^2$             $....... (1)$

Since, the circumference of the circle is reduced by $50\%$.
It means that the radius of the circle is also reduced by $50\%$.

Then,
The new radius $=0.5r$

Therefore, the new area
$=\pi (0.5r)^2$
$=0.25\pi r^2$

Therefore, the required $\%$
$=\dfrac{\pi r^2-0.25\pi r^2}{\pi r^2}\times 100$
$=\dfrac{0.75\pi r^2}{\pi r^2}\times 100$
$=75\%$

Hence, this is the answer.