Tag: area of a sector of a circle

Questions Related to area of a sector of a circle

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

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

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

  1. $\displaystyle 13.2:m^{2}$

  2. $\displaystyle 14.2:m^{2}$

  3. $\displaystyle 13.4:m^{2}$

  4. $\displaystyle 14.4:m^{2}$

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Correct Option: A
Explanation:

Area of sector $\displaystyle =\frac{42}{360}\times \pi r^{2}$
$\displaystyle =\frac{42}{360}\times \frac{22}{7}\times6\times6=13.2m^{2}$

The area of a sector of a circle of radius $16$ cm cut off by an arc which is $18.5$ cm long is 

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

  1. $168$ cm$\displaystyle ^{2}$

  2. $148$ cm$\displaystyle ^{2}$

  3. $154$ cm$\displaystyle ^{2}$

  4. $176$ cm$\displaystyle ^{2}$

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Correct Option: B
Explanation:

$\displaystyle A=\frac{1}{2}l r=\frac{1}{2}\times 18.5\times 16=148cm^{2}$

A sector of $120^{\circ}$ cut out from a circle has an area of $9\displaystyle \frac {3}{7}$ sq cm. The radius of the circle is

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

  1. $3$ cm

  2. $2.5$ cm

  3. $3.5$ cm

  4. $3.6$ cm

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Correct Option: A
Explanation:

Given, area of an sector $=9\dfrac {3}{7}$ sq. cm , $\theta=120^0$
We know Area of sector $=\dfrac {\theta}{360}\times \pi r^2$
$\Rightarrow \displaystyle \frac {\theta}{360}\, \times\, \pi r^2\, =\, 9\, \displaystyle \frac {3}{7}$
$\Rightarrow \displaystyle \frac {120}{360}\, \times\, \displaystyle \frac {22}{7}\, \times\, r^2\, =\, \displaystyle \frac {66}{7}$
$\Rightarrow r^2\, =\, \displaystyle \frac {66}{7}\, \times\, \displaystyle \frac {360}{120}\, \times\, \displaystyle \frac {7}{22}\, =\, 9$
$\Rightarrow r\, =\, \sqrt 9\, =\, 3$ cm

The area of the sector of a circle, whose radius is $6$ m when the angle at the centre is $42^0$, is

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

  1. $13.2$ sq. m

  2. $14.2$ sq. m

  3. $13.4$ sq.m

  4. $14.4$ sq. m

Show answer
Correct Option: A
Explanation:
Given, $\theta=42^0$, radius $=6$ m
Area of sector $=\, \displaystyle \frac {\theta}{360}\, \times\, \pi r^2$
$=\displaystyle \frac {42}{360}\, \times\, \displaystyle \frac {22}{7}\, \times\, 6\, \times\,6$
$ =\, 13.2$ sq. m

A sector of $120^{\circ}$ cut out from a circle has an area of $9\displaystyle \frac{3}{7}$sq cm. The radius of the circle is

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

  1. $3 cm$

  2. $2.5 cm$

  3. $3.5 cm$

  4. $3.6 cm$

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Correct Option: A
Explanation:
Let radius of circle be $'r' cm$. Then,
$\cfrac { \theta  }{ 360° } \times \pi { r }^{ 2 }=9\cfrac { 3 }{ 7 } cm^2=\cfrac { 66 }{ 7 } cm^2$
$\Rightarrow \cfrac { 120° }{ 360° } \times \cfrac { 22 }{ 7 } \times { r }^{ 2 }=\cfrac { 66 }{ 7 } \Rightarrow { r }^{ 2 }=\cfrac { 66\times 7\times 360° }{ 120°\times 22\times 7 } =9$
$\Rightarrow r=\sqrt { 9 } =3 cm$

The minute hand of a clock is $10$ cm long. Find the area of the face of the clock described by the minute hand between $9$A.M and $9.35$A.M.

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

  1. $90.165cm^2$

  2. $112.6cm^2$

  3. $156.4cm^2$

  4. $183.3cm^2$

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Correct Option: D
Explanation:

We have,
Angle described by the minute hand in one minute $=6^o$


$\therefore$ Angle described by the minute hand in $35$ minutes $=(6\times 35)^o=210^o$

$\therefore$ Area swept by the minute hand in $35$ minutes.


$=$ Area of a sector of angle $210^o$ in a circle of radius $10$ cm

 $=\dfrac {\theta}{360} \pi {r _1}^2$

$= \dfrac{210}{360}\times \dfrac{22}{7}\times (10)^2\ cm^2$.....

$=183.3\ cm^2$

The minute hand of a clock is 7 cm long Find the area  traced out by the minute hand of the clock between 6 pm to 6:30 pm

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

  1. $\displaystyle 14.4cm^{2}$

  2. $\displaystyle 15.4cm^{2}$

  3. $\displaystyle 7.2cm^{2}$

  4. $\displaystyle 6.42cm^{2}$

Show answer
Correct Option: D
Explanation:

The total angle of $ 12 $ hours in a clock is 
$ { 360 }^{ 0 } $.
$ => 24 $ half hours $ = { 360 }^{ 0 } $.
This means for one half an hour, angle $ = \frac {{ 360 }^{ 0 }}{24} = { 15 }^{ 0 } $

Area of a sector of a circle of radius 'r' and angle 
$ \theta = \frac { \theta  }{ 360 } \pi {r}^{2}$
Hence, area of the sector of the circle of  radius $ 7 $ cm and angle $

{ 15 }^{ 0 } = \frac { 15 }{ 360 } \times \frac { 22 }{ 7 } \times 7 \times

7\quad = 6.42  {cm}^{2} $