Question

if the central angle of a sector is $\frac{\pi}{4}$ radians and the radius is 8 meters, what is the area of the sector?
a. 8π square meters
b. 32π square meters
c. 64π square meters
d. 16π square meters

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector is \(A=\frac{1}{2}r^{2}\theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.

Step2: Substitute the given values into the formula

Given \(r = 8\) meters and \(\theta=\frac{\pi}{4}\) radians. Then \(A=\frac{1}{2}\times(8)^{2}\times\frac{\pi}{4}\).
First, calculate \((8)^{2}=64\). Then the expression becomes \(\frac{1}{2}\times64\times\frac{\pi}{4}\).
\(\frac{1}{2}\times64 = 32\), and \(32\times\frac{\pi}{4}=8\pi\).

Answer:

A. \(8\pi\) square meters