Tag: area of sectors and segments

Questions Related to area of sectors and segments

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


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