Question

What is the central angle measure of the sector in radians

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

A = 48π cm²

r = 16 cm

θ = ?

Step 02:

`A\text{ = }(\theta\cdot r^2)/(2)`
`\begin{gathered} 48\pi=(\theta\cdot16^2)/(2) \\ (48\pi\cdot2)/(16^2)=\theta \end{gathered}`
`(96\pi)/(256)=\theta`
`(3\pi)/(8)=\theta`

The answer is:

θ = 3 π / 8