Question

find the area of this sector if ( r=\frac{8}{3} ) and ( \theta=\frac{pi}{2} ) 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 \(r = \frac{8}{3}\) and \(\theta=\frac{\pi}{2}\).

$$
LATEXBLOCK0
$$

Step3: Simplify the expression

$$
LATEXBLOCK1
$$

Answer:

\(\frac{16\pi}{9}\)