Tag: area of sectors and segments

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Questions Related to area of sectors and segments

Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle 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?

  1. $\dfrac{1}{3}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{1}{5}$
  4. $\dfrac{1}{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Area of sector = (1/2) * r^2 * x. Arc length = r * x. Given: (1/2) * r^2 * x = (r * x)^2. This simplifies to (1/2) * r^2 * x = r^2 * x^2. Dividing by r^2 * x (assuming x is not 0), we get 1/2 = x.

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

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 :

  1. $\pi -2$
  2. $\pi -3$

  3. 4
  4. $\pi +2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a geometry problem involving a circle inscribed in a right triangle. The sector area outside the triangle is calculated based on the geometry of the circle touching the sides. The result is pi - 2.

Multiple choice maths circle measures area of a sector of a circle sector and arc of a circle area of sectors and segments
The radius of a circle is $7 cm$, then area of the sector of this circle if the corresponding angle is $30^{\circ}$ is 
  1. $12.83 \,cm^2$
  2. $11.83 \,cm^2$
  3. $12.25 \,cm^2$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
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} $

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

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

  1. $88.83 \,cm^2$
  2. $87.83 \,cm^2$
  3. $89.83 \,cm^2$
  4. $86.83 \,cm^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
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} $


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

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.

  1. 282.6c$m^2$
  2. 200.6c$m^2$
  3. 180.04c$m^2$
  4. 1220.09c$m^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
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
= $314 - 31.4 cm^2$
= $282.6$ $cm^2$

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

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.

  1. $2.2cm$
  2. $4.2cm$
  3. $5.1cm$
  4. $6.2cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 =$2\pi r\dfrac{\theta}{360}$
                                   =$2\times \dfrac{22}{7}\times 3.5\times \dfrac{36}{360}$
                                   =$2.2cm$

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

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

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
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,
$Area=\pi(8)^2\dfrac{210}{360}$
        $=\dfrac{22}{7}\times 8\times 8\times \dfrac{210}{360}$
        $=117\dfrac{1}{3} cm^2$