Question

find the area of this sector if ( r=\frac{3}{4} ) and ( \theta=\frac{pi}{3} ) 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 \(r = \frac{3}{4}\) and \(\theta=\frac{\pi}{3}\).
First, calculate \(r^{2}\): \(r^{2}=(\frac{3}{4})^{2}=\frac{9}{16}\).
Then, substitute into the formula: \(A=\frac{1}{2}\times\frac{9}{16}\times\frac{\pi}{3}\).

Step3: Simplify the expression

$$
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$$

Answer:

\(\frac{3}{32}\)