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

Radius of a marry-go-round is $7\ m$. At its edge, at equal distances swings are suspended. If length of an arc between two successive swings is $4$ metre, then find the number of swings that marry-go-round has.

  1. $13\ swings$.
  2. $11\ swings$.
  3. $15\ swings$.

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

Radius of the merry go round, r = 7m

Perimeter of the merry go round = 2 x pi x r = 2 x 22 / 7 x 7 = 44 m
Arc distance between two swings = 4 m
Hence nos. of swings, n on a circle, should satisfy the following equation:
nx arc distance between two swings = Perimeter of the merry go round
Hence, n x 4 = 44
Hence, n = 44/4 = 11
Hence there are 11 swings on the merry go round.
Correct answer is option (B)

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

Area of the largest triangle that can be inscribed in a semi-circle of radius $r$ units is

  1. $r^2$ sq. units
  2. $\dfrac{1}{2} r^2$ sq. units
  3. $2r^2$ sq. units
  4. $\sqrt{2} r^2$ sq. units
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a triangle is equal to the base times the height.
In a semi circle, the diameter is the base of the semi-circle.
This is equal to $2\times r$ (r = the radius)
If the triangle is an isosceles triangle with an angle of $45^\circ$ at each end, then the height of the triangle is also a radius of the circle.
A = $\frac{1}{2} \times b \times h$ formula for the area of a triangle becomes
A = $\frac{1}{2}\times 2 \times r \times r$ because:
The base of the triangle is equal to $2\times r$
The height of the triangle is equal to r
A = $\frac{1}{2} \times 2 \times r \times r$ becomes:
A = $r^2$

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

If a circular grass lawn of $35\ m$ in radius has a path $7\ m$ wide running around it on the outside, then the area of the path is

  1. $1450\ m^2$
  2. $1576\ m^2$
  3. $1694\ m^2$
  4. $3368\ m^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Radius of bigger circle(with the path) = $35 + 7 = 42\ m.$
Thus area of the path $=$ Area of bigger circle $-$ Area of smaller circle
$\therefore$ Required area $= \pi (42)^2 - \pi (35)^2 = \dfrac{22}{7} \times (42 + 35)(42 - 35) = 22 \times 77 = 1694\ m^2$

Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

The outer and inner diameters of a circular pipe are $6$ cm and $4$ cm respectively. If its length is $10$ cm then what is the total surface area in square centimetres?

  1. $55\pi$
  2. $110\pi$
  3. $150\pi$

  4. None of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given, outer and inner diameters of circular pipe are $6$ cm and $4$ cm
Therefore, outer and inner radii of a circular pipe are $3$ cm and $2$ cm.
Thus total surface area would be $ 10\times \pi (3^{2} - 2^{2})$ $= 50\pi $ sq. cm.

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

Tick the correct answer in the following:
Area of a sector of angle $\theta$ (in degrees) of a circle with radius R is

  1. $\dfrac {\theta}{180}\times 2\pi R$
  2. $\dfrac {\theta}{180}\times \pi R^{2}$
  3. $\dfrac {\theta}{3600}\times 2\pi R$
  4. $\dfrac {\theta}{720}\times 2\pi R^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Area of a sector with angle $p$ $=\dfrac{\theta}{360}\times\pi R^2$

$=\dfrac{\theta}{360\times2}\times\pi R^2\times2$

$=\dfrac{\theta}{720}\times2\pi R^2$

Hence, Option $D$ is correct

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

The perimeter of a sector of a circle is $56$ cms and the area of the circle is $64\pi$ sq. cms  Find the area of sector.

  1. $360cm^2$
  2. $160cm^2$
  3. $260cm^2$

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

Area $= \pi r^{2}=64\pi cm^{2}$  


$\Rightarrow r=8cm$ 


perimeter $=2r+r\theta $ 

perimeter of sector $=r(\theta +2)=56cm$ 

$\Rightarrow \theta =5rad$ 

Area of sector $=\dfrac{r^{2}\theta }{2}=\dfrac{64}{2}\times 5cm^{2}$

                        $=160cm^{2}$

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

In a circle with radius $5.7\ cm$, the perimeter of a sector is $27.2\ cm$. Find the area of this sector.

  1. $97.52cm^2$
  2. $57.52cm^2$
  3. $77.52cm^2$
  4. $87.52cm^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$R=5.7 cm$
Perimeter = $R\theta =27.2 cm$
$\therefore R\theta = 27.2 cm$
$\theta = \left(\dfrac{27.2}{5.7}\right)^{c}$
$\therefore $ Area of sector $=\dfrac{1}{2}R^{2}\theta $
$=\dfrac{1}{2}\times (5.7)^{2}\times \dfrac{27.2}{5.7}$
$=\dfrac{5.7}{2}\times 27.2 cm^{2}$
$ = 5.7 \times 13.6 = 77.52 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

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

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

Area of sector $=$ $\dfrac { \theta  }{ { 360 }^{ 0 } } \times \pi { r }^{ 2 }=\dfrac { { 42 }^{ 0 } }{ { 360 }^{ 0 } } \times \dfrac { 22 }{ 7 } \times 6\times 6=13.2{ m }^{ 2 }$

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

Area of a sector having radius 12 cm and arc length 21 cm is

  1. 126 $cm^2$
  2. 252 $cm^2$
  3. 33 $cm^2$
  4. 45 $cm^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Arc Length : Perimeter = Area of Sector : Area of Circle

$21: 2\pi r = \; Area \; of \;  Sector : \pi r^2$

$21:24\pi = \; Area \; of \;  Sector :144\pi$

Area of Sector $= \dfrac{144 \pi *21}{24 \pi} = 126cm^2$

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

If the area and arc length of the sector of a circle are 60 $cm^2$ and 20 cm respectively, then the diameter of the circle is 

  1. 6 cm

  2. 12 cm

  3. 24 cm

  4. 36 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Arc length of the Circle  : Area of the Sector = Perimeter of the Circle :Area of the Circle

Let the radius of the circle be 'r'.

 

Hence, $20 : 60$=$ 2\pi r : \pi r^2$

$ 1:3 = 2: r$

$ r= 6 $ (Product of Means = Product of Extremes)

Therefore, $Diameter = 2r = 12cm$