Question

A sector with a radius of \maroonD{12\,\text{cm}}12cmstart color #ca337c, 12, start text, c, m, end text, end color #ca337c has an area of \goldE{60\pi\,\text{cm}^2}60πcm 2 start color #a75a05, 60, pi, start text, c, m, end text, squared, end color #a75a05. What is the central angle measure of the sector in radians?

Answer 1

9514 1404 393

Answer:

5π/6 radians

Explanation:

Given:

a sector with radius 12 cm and area 60π cm²

Find:

the central angle measure in radians

Solution:

The area is given by the formula ...

A = (1/2)r²θ

Then the angle is ...

θ = 2A/r² = 2(60π cm²)/(12 cm)² = 120/144π = 5π/6

The central angle is 5π/6 radians.