Question

Area of a sector of the circle is 1/6 times the area of the circle. Find the angle
subtended at the centre by the given sector.​

Answer 1

Answer:

Given:

Area of a sector of the circle is 1/6 times the area of the circle.

Let us consider the angle subtended as "A".

Area of a sector =(1/6) area of the circle.

(A× πr²)/360 = (1/6) πr²

A /360 = 1/6

A = 360/6

A = 60°

Therefore, angle

subtended at the centre by the given sector is 60°.

Answer 2

Answer:

let the radius of the sector of the circle be r and angle substended by it at the centre be theta

according to question,

area of sector = 1/6 of area of circle

theta/ 360× πr2 = 1/6× πr2

theta = 360/6

theta = 60°