Length of Arc of a Sector

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

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)/60

3. (πrθ)/360

4. (πrθ)/90

Q.

1. x = (y × θ)/360

2. x = (y × θ)/180

3. y = (x × θ)/360

4. y = (x × θ)/260

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. ${36}^{\circ }$

2. ${45}^{\circ }$

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

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

Q.

The perimeter of a sector of circle with radius 5.7 m is 27.2 m. The length of the arc of sector (in m) is _______.

1. 13.4

2. 16.9

3. 15.8

4. 14.1

Q.

State true or false.
If the diameter of a semi-circular protractor is 14 cm then the perimeter will be 36 cm(Approx.)

1. 35

2. 36

Q.

A pendulum swings through an angle of ${30}^{\circ }$ and describes an arc 8.8 cm in length. Find the length of pendulum in cm.

1. 14.5

2. 15.1

3. 17.3

4. 16.8

Q.

The area in $c{m}^2$ of a quadrant of a circle whose circumference is 22 cm is _______

1. 16

2. 15

3. 9.6

4. 155

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.

The given figure is a sector of a circle of radius 20 cm. Find the perimeter of the sector.
(Take $\pi$ = 3.14)

1. 55.25 cm

2. 60.93 cm

3. 65.48 cm

4. 70.17