Question

A sector with an area of \goldE{48\pi,\text{cm}^2}48πcm 2 start color #a75a05, 48, pi, start text, c, m, end text, squared, end color #a75a05 has a radius of \maroonD{16,\text{cm}}16cmstart color #ca337c, 16, start text, c, m, end text, end color #ca337c. What is the central angle measure of the sector in radians? Choose 1 answer: Choose 1 answer:

Answer 1

3/8 π radians

Explanation:

The Area of a sector when then central angle is in radians = 1/2r² θ

Where

θ = central angle = ?

r = 16 cm

Area of the sector = 48πcm²

Hence

Central angle = Area of a sector ÷ (1/2r²)

= 48πcm² ÷ (1/2 × 16²)

= 48πcm² ÷ 128

Central angle = 3/8π radians

Therefore, Central angle = 3/8π radians