Question

A sector with an area of 140 pi cm2 has a radius of 20cm

What is the central angle measure of the sector in degrees?

Answer 1

Answer: The central angle measure is 126°

Explanation:

The circle has a radius of 20cm

The area of a sector of a circle of an angle A is:

Area = (A/360°)*pi*r^2

where r is the radius.

Here we have that the area is (140*pi) cm^2

let's find the value of A.

(140*pi) cm^2 = (A/360)*pi*(20cm)^2 = (A/360)*pi*400cm^2

140 cm^2 = (A/360)*400 cm^2

A = (140/400)*360° = 126°

The central angle measure is 126°