find the area of this sector if ( r=\frac{2}{3} ) and ( heta=\frac{pi}{6} ) radians. ( \frac{pi}{?} ) sq units

Question

find the area of this sector if ( r=\frac{2}{3} ) and ( 	heta=\frac{pi}{6} ) radians. ( \frac{pi}{?} ) sq units

Accepted Answer

# 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 $r = \frac{2}{3}$ and $\theta=\frac{\pi}{6}$.
Substitute into $A=\frac{1}{2}r^{2}\theta$:
$$
\begin{align*}
A&=\frac{1}{2}\times(\frac{2}{3})^{2}\times\frac{\pi}{6}\
&=\frac{1}{2}\times\frac{4}{9}\times\frac{\pi}{6}\
\end{align*}
$$
## Step3: Simplify the expression
$$
\begin{align*}
A&=\frac{1\times4\times\pi}{2\times9\times6}\
&=\frac{4\pi}{108}\
&=\frac{\pi}{27}
\end{align*}
$$

# Answer:
$\frac{\pi}{27}$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the area of a sector

Step2: Substitute the given values into the formula

Step3: Simplify the expression

Answer: