Question

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3
use the keypad to enter your answer in the box. express your answer in terms of $pi$.
$a=square cm^{2}$

Explanation:

Step1: Recall sector - area formula

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

Step2: Identify values of $r$ and $\theta$

Given that $r = 10$ cm and $\theta=\frac{\pi}{5}$ rad.

Step3: Substitute values into formula

Substitute $r = 10$ and $\theta=\frac{\pi}{5}$ into the formula $A=\frac{1}{2}r^{2}\theta$. We get $A=\frac{1}{2}\times(10)^{2}\times\frac{\pi}{5}$.

Step4: Simplify the expression

First, $(10)^{2}=100$. Then $\frac{1}{2}\times100\times\frac{\pi}{5}= \frac{100\pi}{10}=10\pi$.

Answer:

$10\pi$