Length of an Arc

Q. Question 15
Area of sector of central angle ${200}^{\circ }$ of a circle is $770c{m}^2$. Find the length of the corresponding arc of this sector.

Q. Find the area of the shaded sector of the circle having radius = 21 cm. (Use $=\pi \frac{22}{7}$)

1. $192.5c{m}^2$
2. $385c{m}^2$
3. $462c{m}^2$
4. $539c{m}^2$

Q. Question 16
A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of ${60}^{\circ }$ at its centre. Find the radius of the circle.

Q. A field is to be fenced on its boundary to protect its crop from animals roaming around. The field is shown in the following figure as a shaded region. If the rate of fencing is ₹ 25/m, then the total cost of fencing is ₹_____. (Use $\pi =\frac{22}{7}$)

1. 800.00
2. 1044.5
3. 41.78
4. 244.50

Q. Find the area of the shaded segment.

1. $11$
2. $12$
3. $13$
4. $14$

Q.

What is the relation between $\widehat{BC}$ and $\widehat{AD}$?

1. $\widehat{BC}=\widehat{AD}$

2. $\widehat{BC}>\widehat{AD}$

3. $\widehat{BC}=2\widehat{AD}$

4. $\widehat{BC}<\widehat{AD}$

Q. The circumference of a circle is 8 cm. Find the area of the sector whose central angle is 72${}^{\circ }$.

Q.

The length of the minute hand of a clock is 14 cm. Find the area in ${cm}^2$ swept by the minute hand in 5 minutes.

1. 51.3

2. 55.1

3. 60.2

4. 70.8

Q. AB and PQ are two equal chords of a circle. If the length of minor arc and major arc formed by AB is 24cm and 64cm, respectively, then find the length of minor and major arc formed by PQ.

Q.

What is the arc length of a circle that has a $7\mathrm{cm}$ radius and a central angle that is $40°$? Use $3.14$ for $\pi$ and round your answer to the nearest hundredth.

Q. A circle has radius 5 cm. A section of its circumference has length $\pi$ cm, then the angle subtended by this section at the centre is

1. ${36}^{\circ }$
2. ${45}^{\circ }$
3. ${50}^{\circ }$

Q. A circle has radius 5 cm. A section of its circumference has length $\pi$ cm, then the angle subtended by this section at the centre is

1. ${36}^{\circ }$
2. ${45}^{\circ }$
3. ${50}^{\circ }$

Q.

The length of the minute hand of a clock is 14 cm. Find the area in ${cm}^2$ swept by the minute hand in 5 minutes.

1. 51.3

2. 55.1

3. 60.2

4. 70.8

Q. A chord PQ of a circle with a radius of 15 cm subtends an angle of ${60}^{\circ }$ with the center of the circle. Find the area of the minor as well as the major segment. $(\pi =3.14,\sqrt{3}=1.73)$

Q.

AB and PQ are two equal chords of a circle. If the length of minor arc and major arc formed by AB is 24cm and 64cm respectively, then the length of minor and major arc formed by PQ is ___ and ___ respectively.

1. 64 cm, 24 cm

2. 24 cm, 64 cm

3. 32 cm, 12 cm

4. 12 cm, 32 cm

Q.

The length of the minute hand of a clock is 14 cm. Find the area in ${cm}^2$ swept by the minute hand in 5 minutes.

1. 51.3

2. 55.1

3. 60.2

4. 70.8