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?

Answer 1

3pi/8

Explanation:

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Answer 2

`\theta=(3\pi)/(8) $ (in radians)`

Explanation:

Area of a sector
`=(\theta)/(2\pi)X\pi r^2`

Given: Area of a sector
`=48\pi cm^2`

Radius of the circle =16cm

Therefore:

`48\pi cm^2=(\theta)/(2)X 16^2\\256\theta=96\pi\\\theta=(96\pi)/(256) \\\theta=(3\pi)/(8) $ (in radians)\\Therefore, the central angle \theta=(3\pi)/(8) $ (in radians)`