Length of Arc of Sector

Q.

What is the length of an arc which subtends angle $\theta$ (degrees) at the centre in a circle of radius r?

1. (πrθ)/180

2. (πrθ)/360

3. (πrθ)/90

4. (πrθ)/60

Q.

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

1. ${45}^{\circ }$

2. ${36}^{\circ }$

3. ${50}^{\circ }$

4. ${60}^{\circ }$

Q.

There is a circular swimming pool. There is a bob at the centre of the pool at a distance of $\frac{50}{\pi }$ m from the pool’s wall. Shyam is standing next to the

wall and holding a thread whose other end is connected to the heavy stationary bob at the centre. Holding the thread Shyam now moves along the wall for 20

seconds and the angle between the initial and final positions of the thread is ${12}^{\circ }$. What is Shyam’s speed in metres/minute?

1. 1

2. 5

3. 10

4. 20

Q.

For a circle of radius $r=\frac{10}{\pi }$ cm.
Angle subtended by arc $\theta ={12}^{\circ }$ .
What is the length of the arc in cm?

1. $\frac{2}{3}cm$

2. $\frac{1}{3}cm$

3. $\frac{3}{2}cm$

4. 2 cm

Q. A wire is bent to form a circle of radius 7 cm. From the resulting shape, a chunk of the wire is cut off, and the wire cut off measures 4 cm in length. The length of the remaining wire is ___ cm