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{ = }\frac{\theta\cdot r^2}{2}$$\begin{gathered} 48\pi=\frac{\theta\cdot16^2}{2} \\ \frac{48\pi\cdot2}{16^2}=\theta \end{gathered}$$\frac{96\pi}{256}=\theta$$\frac{3\pi}{8}=\theta$

The answer is:

θ = 3 π / 8