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

The radius of a circle is $5: m$. Find the circumference of the circle whose area is $49$ times the area of the given circle.

  1. $220 \: m$
  2. $120 \: m$
  3. $320 \: m$
  4. $420 \: m$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Radius of given circle $=5\ cm$
Therefore,
Area of given circle $=\pi (5)^2$
                              $=25\pi\ cm^2$
Let radius of required circle $ =r$
Therefore,
$\pi r^2=49\times 25\pi$
$\Rightarrow r^2=(7\times 5)^2$
$\Rightarrow r=35$
Therefore,
Circumference $=2\pi r$
                       $=2\times \frac { 22 }{ 7 }\times35$
                       $=220\ m$
Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

Find the area of a ring whose outer and inner radii are $19\ cm$ and $16\ cm$ respectively.

  1. $330\ cm^2$
  2. $310\ cm^2$
  3. $320\ cm^2$
  4. $350\ cm^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of outer circle $=\pi{(19)}^2$
                                 $=\cfrac{22}{7}\times 361$
Area of inner circle $=\pi{(16)}^2$
                                 $=\cfrac{22}{7}\times 256$
$\therefore$ area of the ring $=\dfrac{22}{7}\times 361-\dfrac{22}{7}\times 256$
                              $=\cfrac{22}{7}(361-256)$
                              $=\cfrac{22}{7}(105)$
                              $=330\ cm^2$

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

The area enclosed between two concentric circle is $770$ $cm^2$. If the radius of the outer circle is $21$ $cm$, calculate the radius of the inner circle.

  1. $7$ $cm$
  2. $14$ $cm$
  3. $2.1$ $cm$
  4. $35$ $cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let radius of the inner circle be $r$ and radius of the outer circle be $R=21cm$


Area enclosed between the two concentric circles $=\pi(R^2-r^2)=770cm^2$

$\Rightarrow 770=\pi(R^2-r^2)$

$\Rightarrow 770=\dfrac{22}{7}(21^2-r^2)$

$\Rightarrow \dfrac{770\times 7}{22}=441-r^2$

$\Rightarrow 245=441-r^2$

$\Rightarrow r^2=196$

$\Rightarrow r=\sqrt{196}$

$\Rightarrow r=14$

Thus, radius of the inner circle $=14$ $cm$

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 $= \pi (R + r)(R - r)$
$= \cfrac {22}{7} (15 + 13) \times (15 - 13)$
$= \cfrac {22}{7} \times 28 \times 2$
$=176$ sq cm
Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The area of a circular ring between two concentric circles of radii r and (r + h) units respectively is given by

  1. $\pi (2r+h)h\ sq. units$
  2. $\pi (r+h)h\ sq. units$
  3. $\pi (r+2h)h\ sq. units$
  4. $\pi (r-h)h\ sq. units$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
$A = $ area of bigger circle - area of smaller circle
$=\pi (r+h)^2-\pi r^2$
$=\pi(r^2+h^2+2hr-r^2)$
$=\pi(h^2+2hr)$
$=\pi(h+2r)h$
Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

The ratio of the outer and inner circumferences of a circular path is $23:22$, If the path is $5\ m$ wide, the radius of the inner circle is: 

  1. $55\ m$
  2. $110\ m$
  3. $220\ m$
  4. $230\ m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given: $r _1=5+r _2$
$\displaystyle \frac {2\pi r _1}{2\pi r _2}=\frac {23}{22}$

$\displaystyle \Rightarrow \frac {r _1}{r _2}=\frac {23}{22}$

$\displaystyle \Rightarrow \frac {5+r _2}{r _2}=\frac {23}{22}$

$\displaystyle \Rightarrow 110+22r _2=23r _2$

$\displaystyle \Rightarrow r _2=110\ m$
$\therefore $ Radius of inner circle$=110\ m$

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 the outer and inner circumferences of the circular park is $132$ m. Its width is

  1. $20$ m
  2. $21$ m
  3. $22$ m
  4. $24$ m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Let $r _1$ and $C _1$ be the radius and the circumference of the outer circle.
Let $r _2$ and $C _2$ be the radius and the circumference of the inner circle.
The width of the circular path is $(r _1-r _2)$ m.
Given, $C _1-C _2=132$ m
$\Rightarrow 2\pi r _1 - 2\pi r _2=132$
$\Rightarrow 2\pi (r _1-r _2)=132$
$\Rightarrow r _1-r _2=\cfrac{66}{\dfrac{22}{7}}$
$\Rightarrow r _1-r _2=21$
Thus, width of the circular path is $21$ m.
Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

What is the area of the circular ring included between two concentric circles of radius $14$ cm and $10.5$ cm ? 

  1. $255 cm^2$.
  2. $148 cm^2$.
  3. $324 cm^2$.
  4. $269 cm^2$.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

 Area of the circular ring = $\frac { 22 }{ 7 } \times \left( { R }^{ 2 } - { r }^{ 2 } \right)$ = $ \frac { 22 }{ 7 } \times \left( { 14 }^{ 2 } - { 10.5 }^{ 2 } \right)$ = $269.5 \ { cm }^{ 2 }\approx 269\ { cm }^{ 2 } $

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

A semicircle of diameter 2 is drawn. Two point on the semicircle are chosen so that they are 1 unit apart. A  semicircle of diameter 1 is the drawn with those two point as the 'endpoints' . The shaded area inside this smaller semicircle and outside the larger semicircle is called a lune. Determine the area of this lune.

  1. $\frac{\pi }{6} - \frac{{\sqrt 3 }}{4}$
  2. $\frac{{\sqrt 3 }}{4} - \frac{\pi }{{12}}$
  3. $\frac{{\sqrt 3 }}{4} - \frac{\pi }{{24}}$
  4. $\frac{{\sqrt 3 }}{4} + \frac{\pi }{{24}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The lune area is calculated by finding the area of the smaller semicircle and subtracting the overlapping segment area. The geometry involves a 60-degree sector or similar trigonometric relations.

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

Find the area of a ring shaped region enclosed between two concentric circles of radii $20$ cm and $15$ cm.

  1. 550 $cm^{2}$
  2. 425 $cm^{2}$
  3. 496 $cm^{2}$
  4. 810 $cm^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a ring shaped region$=\pi(20)^2-\pi(15)^2$
                                                    $=(400-225)\times \dfrac{22}{7}$
                                                    $=(175)\times \dfrac{22}{7}$
                                                   $ =550$ sq. cm