Question

find the area of this sector if ( r = 3 ) and ( \theta = \frac{pi}{4} ) radians.
( \frac{?}{} pi ) sq units

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 \(r = 3\) and \(\theta=\frac{\pi}{4}\).
Substitute into \(A=\frac{1}{2}r^{2}\theta\):

$$
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Answer:

\(\frac{9\pi}{8}\)