Question

A sector with an area of 30(pi) cm^2 has a radius of 10 cm.

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

Answer 1

The ratio of the angle of the sector to the entire circle is 5/18

The area of the entire circle is 108

Explanation:

Answer 2

108°

Explanation:

The area of a sector is given by the formula ...

A = (1/2)r²θ . . . . . where θ is in radians

Solving for θ, we find ...

θ = 2A/r²

For your given sector, the central angle is ...

θ = 2(30π cm²)/(10 cm)² = 0.6π . . . . radians

π radians is 180°, so the central angle in degrees is ...

θ = (0.6)(180°) = 108°

The central angle measure of the sector is 108°.