Tag: area of a sector of a circle

Questions Related to area of a sector of a circle

Consider a circle with unit radius. There are seven adjacent sectors, $S _{1}, S _{2}, S _{3} ...S _{7}$, in the circle such that their total area is $\dfrac {1}{8}$ of the area of the circle. Further, the area of the $j^{th}$ sector is twice that of the $(j - i)^{th}$ sector, for $j = 2, .... 7$. Find the area of the sector $S _{1}$

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

  1. $\dfrac {\pi}{1016}$

  2. $\dfrac {\pi}{986}$

  3. $\dfrac {\pi}{116}$

  4. None

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Correct Option: A

Find the area of a sector of a circle of radius $28$cm and central angle $45^0$.

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

  1. $616 cm^{2}$

  2. $308 cm^{2}$

  3. $508 cm^{2}$

  4. $154 cm^{2}$

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Correct Option: B
Explanation:

Radius of sector $=28 cm$

Control angle $=45^{ o }$
Area of sector $=\cfrac { \theta  }{ 360° } \times \pi { r }^{ 2 }$
$=\cfrac { 45° }{ 360° } \times \cfrac { 22 }{ 7 } \times 28\times 28\ =308\quad { cm }^{ 2 }$

If a sector of a circle of diameter 21 cm subtends an angle of $120^{\circ}$ at the centre, then what is its area ? 

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

  1. $115.5 \ cm^2$.

  2. $84 \ cm^2$.

  3. $85.5 \ cm^2$.

  4. $78 \ cm^2$.

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Correct Option: A
Explanation:

Area of sector = $\cfrac{120}{360} \times \pi \times (\cfrac{21}{2})^2$

Thus area = $\cfrac{1}{3} \times \cfrac{22}{7} \times \cfrac{441}{4} = 115.5 cm^2$

To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle $80^{\circ}$ to a distance of 16.5 km. The area of the sea over which the ships are warned is 190 $km^2$ (app.).

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

  1. True

  2. False

  3. Nither

  4. Either

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Correct Option: A

If the sector of a circle of diameter $14 cm$ subtends an angle of $30^{\circ}$ at the centre, then its area is

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

  1. $49 \pi$

  2. $\displaystyle \frac{49 \pi}{12}$

  3. $\displaystyle \frac{242}{3\pi}$

  4. $\displaystyle \frac{121}{3\pi}$

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Correct Option: B,D
Explanation:

Area of a sector $=\dfrac{\theta}{360^0} \times \pi r^2 =\dfrac{30}{360} \times \pi (7)^2 = \dfrac{49 \pi}{12}$


Also, 
$ \dfrac{121}{3\pi}=\dfrac{121 \times 7}{3 \times 22} = \dfrac{49 \times 22}{12 \times 7} = \dfrac{49 \pi}{12}$

A circular disc of radius 10 cm is divided into sectors with  angles $120^{\circ}$ and $150^{\circ}$ then  the ratio of the area of two  sectors is

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

  1. 4 : 5

  2. 5 : 4

  3. 2 : 1

  4. 8 : 7

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Correct Option: A
Explanation:

Area of sector formed from angle $\theta$ = $\frac{\theta}{260} \pi r^2$, where r is the radius of the circle
Now, if angle is 120, 150 then the ratio of area of sector will be:
= $\frac{\frac{120}{360} \pi r^2}{\frac{150}{360} \pi r^2}$
= $\frac{120}{150}$ = 4:5

The area of a sector of a circle of angle $\displaystyle 60^{\circ}$ is $\displaystyle \frac{66}{7}cm^{2}$ then the area of the corresponding major sector is

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

  1. $\displaystyle 14cm^{2}$

  2. $\displaystyle \frac{55}{7}cm^{2}$

  3. $\displaystyle \frac{110}{7}cm^{2}$

  4. $\displaystyle \frac{330}{7}cm^2$

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Correct Option: D
Explanation:

Area of a sector of a circle of radius 'r' and angle  $ \theta = \frac {

\theta  }{ 360 } \pi {r}^{2}$
Given, $ \frac { 60 }{ 360 } \times \frac {22}{7} \times {r}^{2} = \frac {66}{7}  {cm}^{2} $
$ {r}^{2} = 18 $
Now, area of sector with angle {300}^{o} $ = \frac

{ 300 }{ 360 } \times \frac {22}{7} \times {r}^{2} = \frac

{ 300 }{ 360 } \times \frac {22}{7} \times 18 = \frac {330}{7}  {cm}^{2} $




A Car has two wipers which do not cover mutual area. Length of each wiper is 25 cms and it makes angle of $\displaystyle 115^{\circ}$ while cleaning. The area of cleaning by the wiper in one movement will be-

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

  1. $\displaystyle \frac{152815}{126}cm^{2}$

  2. $\displaystyle \frac{185125}{128}cm^{2}$

  3. $\displaystyle \frac{215815}{126}cm^{2}$

  4. $\displaystyle \frac{158125}{126}cm^{2}$

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Correct Option: D
Explanation:

Required area $\displaystyle =2\times \frac{115^{\circ}}{360^{\circ}}\pi \left ( 25 \right )^{2}$
$\displaystyle =2\times \frac{115}{360}\times \frac{22}{7}\times 625$


$\displaystyle=\frac{158125}{126}cm^{2}$