Area of a Sector

Q. Find the area of the sector of a circle if the radius of the circle is 5 cm, and the length of the arc is 4 cm.

1. $10{\text{cm}}^2$
2. $5{\text{cm}}^2$
3. $20{\text{cm}}^2$
4. $15{\text{cm}}^2$

Q. If the area of a sector is one fourth of the area of the circle, then the angle of the sector is:

1. ${180}^{\circ }$
2. ${40}^{\circ }$
3. ${45}^{\circ }$
4. ${90}^{\circ }$

Q. Find the length of the arc which is part of a sector whose area is 77 $c{m}^2$ and the radius of the circle is 7 cm.

1. 11 cm
2. 22 cm
3. 66 cm
4. 44 cm

Q. If $\theta ={60}^{\circ }$, what would be the value of area of the sector of the circle of radius $r$?

1. $\pi r^2$
2. $\frac{1}{3}\pi r^2$
   
3. $\frac{1}{6}\pi r^2$
   
4. $\frac{1}{2}\pi r^2$
   

Q.

The area in $c{m}^2$ of a sector of a circle with radius 6 cm if angle of the sector is ${60}^{\circ }$ is ___ $c{m}^2$.

Q. What is the area of a sector whose arc subtends a ${30}^{\circ }$ angle at the center of a circle of radius 12 inches?

1. $144\pi inche{s}^2$
2. $12\pi inche{s}^2$
3. $6\pi inche{s}^2$
4. $24\pi inche{s}^2$

Q. Find the area of shaded region, if in parallelogram ABCD, $\angle$PBQ=$\angle$SDR = ${60}^o$, BP=BQ=SD=RD= 21 cm, BC = 45 cm and MN = 20 cm.

1. 438 $c{m}^2$
2. 231 $c{m}^2$
3. 897 $c{m}^2$
4. 669 $c{m}^2$

Q. If the area and the perimeter of a sector of a circle are $12{\text{cm}}^2$ and $14\text{cm}$ respectively, then possible values of:

1. $\text{radius of the circle = 6 cm, length of the arc = 8 cm}$
2. $\text{radius of the circle = 3 cm, length of the arc = 4 cm}$
3. $\text{radius of the circle = 4 cm, length of the arc = 6 cm}$
4. $\text{radius of the circle = 3 cm, length of the arc = 8 cm}$

Q. Earthworms decide to protest against the climate change. They occupy an area where no humans can come.
The earthworms occupy the 'Green' coloured portion as shown in the figure. Find the area of the green portion that earthworms occupy. (Take $\pi =\frac{22}{7}$)

1. $196mile{s}^2$
2. $154mile{s}^2$
3. $42mile{s}^2$
4. $350mile{s}^2$

Q. If radius is 14 cm and angle at centre of circle is 180 degree, then length of the arc is ___ .

1. 54 cm
2. 24 cm
3. 34 cm
4. 44 cm

Q.

Find the area of the sector whose arc is making an angle of ${60}^{\circ }$ at the center of a circle of radius 3.2 cm. What will be the area of the balance sector? [3 MARKS]

Q. If $f\left(9\right)=9$ and $f^{\prime }\left(9\right)=4$, then $\underset{x\to 9}{lim}\frac{\sqrt{f\left(x\right)}-3}{\sqrt{x}-3}$ is equal to

Q. If the angle of the sector with radius 3 cm is ${120}^{\circ }$, then its area is:

1. $2\pi {\text{cm}}^2$
2. $3\pi {\text{cm}}^2$
3. $\pi {\text{cm}}^2$
4. $6\pi {\text{cm}}^2$