Question

A sector has radius 8 and central angle 172°. Find the area of the sector.

Answer 1

Answer

Explanation

Given:

radius = 8

central angle =172°

To determine the area of the sector, we use the formula:

$A=\frac{central\text{ angle}\degree}{360\degree}(\pi)r^2$

where:

central angle =172°

r=radius = 8

A=Area

We plug in what we know:

$\begin{gathered} A=\frac{central\text{ angle}\operatorname{\degree}}{360\operatorname{\degree}}(\pi)r^2 \\ =\frac{172\degree}{360\degree}(\pi)(8)^2 \\ Simplify \\ A=96.06\text{ square units} \end{gathered}$

Therefore, the area of the sector is 96.06 square units.