Tag: area of sectors and segments

Questions Related to area of sectors and segments

An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that the area of the sector AOB is equal to the square of the length of the arc AB, then the value of x?

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

  1. $\dfrac{1}{3}$

  2. $\dfrac{1}{4}$

  3. $\dfrac{1}{5}$

  4. $\dfrac{1}{2}$

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Correct Option: D

A wire of length $20\ cm$ can be bent $n$ the form of a sector then its maximum area is 

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

  1. $15\ sq.cm$

  2. $25\ sq.cm$

  3. $5\ sq.cm$

  4. $none$

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Correct Option: A

ABC is a right angel triangle right angled at vertex A. A circle is drawn to touch sides AB and AC at points P and Q respectively such that other end points of diameters passing through P and Q lie on side BC. If AB = 6. then the area of circular sector which lies outside the triangle is :

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

  1. $\pi -2$

  2. $\pi -3$

  3. 4

  4. $\pi +2$

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Correct Option: A

The area of the sector of circle ${x}^{2}+{y}^{2}=16$ and the line $y=x$ in the first quadrant is 

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

  1. $8\pi sq.units$

  2. $\pi sq.units$

  3. $4\pi sq.units$

  4. $2\pi sq.units$

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Correct Option: A

The area of a sector whose perimeter is four times its radius (r units)is

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

  1. $\sqrt{r}\,sq.\,units$

  2. ${r}^{4}\,sq.\,units$

  3. ${r}^{2}\,sq.\,units$

  4. $\displaystyle \frac {{r}^{2}}{r}\,sq.\,units$

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Correct Option: A
The radius of a circle is $7 cm$, then area of the sector of this circle if the corresponding angle is $30^{\circ}$ is 
maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments

  1. $12.83 \,cm^2$

  2. $11.83 \,cm^2$

  3. $12.25 \,cm^2$

  4. None of these

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Correct Option: A
Explanation:

Area of a sector of a circle of radius '$r$' and angle $ = \dfrac { \theta  }{ 360 } \pi {r}^{2}$
Hence, area of the sector of the circle of  radius $ 7 $ cm and angle $ = \dfrac { 30 }{ 360 } \times \dfrac { 22 }{ 7 } \times 7 \times 7 = 12.83 \ \text{cm}^{2} $

The radius of a circle is $7 cm$, then area of the sector of this circle if the corresponding angle is:$210^{\circ}$ is 

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

  1. $88.83 \,cm^2$

  2. $87.83 \,cm^2$

  3. $89.83 \,cm^2$

  4. $86.83 \,cm^2$

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Correct Option: C
Explanation:

Area of a sector of a circle of radius 'r' and angle  $ \theta = \dfrac { \theta  }{ 360 } \pi {r}^{2}$

Hence,area of the sector of the circle of  radius $ 7 $ cm and angle $ { 210 }^{

0 } = \dfrac { 210 }{ 360 } \times \dfrac { 22 }{ 7 } \times 7 \times

7\quad = 89.83  {cm}^{2} $


The area of a circle is 314 sq. cm and area of its minor sector is 31.4 sq. cm. Find the area of its major sector.

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

  1. 282.6c$m^2$

  2. 200.6c$m^2$

  3. 180.04c$m^2$

  4. 1220.09c$m^2$

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Correct Option: A
Explanation:

Given:
Area of circle = $314 $$cm^2$
Area of minor sector = $31.4 $$cm^2$
Area of major sector = Area of a circle - Area of minor sector
= $314 - 31.4 cm^2$
= $282.6$ $cm^2$

The radius of a circle is $3.5$ cm and area of the sector is $3.85$ $cm^2$. Find the length of the corresponding arc.

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

  1. $2.2cm$

  2. $4.2cm$

  3. $5.1cm$

  4. $6.2cm$

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Correct Option: A
Explanation:

Let the angle of centre made by the sector be $\theta$
Therefore,
Area of the sector=$\pi r^2\dfrac{\theta }{360}$
                        $=>3.85=\dfrac{\pi(3.5)^2\theta}{360}$


                        $=>\theta=\dfrac{3.8\times 360\times 7}{(3.5)^2\times 22}$
                        $=35.5$
                        $=36$
Thus length of the arc =$2\pi r\dfrac{\theta}{360}$
                                   =$2\times \dfrac{22}{7}\times 3.5\times \dfrac{36}{360}$
                                   =$2.2cm$

The minute hand of a clock is $8: cm$ long. Find the area swept by the minute hand between $8.30: a.m.$ and $9.05: a.m.$

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

  1. $\displaystyle 117\frac{1}{3}:cm^{2}$

  2. $\displaystyle 107\frac{1}{3}:cm^{2}$

  3. $\displaystyle 217\frac{1}{3}:cm^{2}$

  4. None of these

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Correct Option: A
Explanation:

Angle made the centre by each $5$ minutes =$\dfrac{360}{12}$
                                                              =$30^o$


Angle covered between $8.30$am to $9.5$a.m is $210^o$

Therefore,
$Area=\pi(8)^2\dfrac{210}{360}$
        $=\dfrac{22}{7}\times 8\times 8\times \dfrac{210}{360}$
        $=117\dfrac{1}{3} cm^2$