a sector of a circle has a central angle of 150°. find the area of the sector if the radius of the circle is 5 cm. cm² add work check answer

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Accepted Answer

# Explanation:
## Step1: Recall the formula for the area of a sector
The formula for the area of a sector of a circle is $A=\frac{\theta}{360}\times\pi r^{2}$, where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.
## Step2: Substitute the given values into the formula
Given $\theta = 150^{\circ}$ and $r = 5\space cm$.
$$
\begin{align*}
A&=\frac{150}{360}\times\pi\times(5)^{2}\
&=\frac{5}{12}\times\pi\times25\
&=\frac{125\pi}{12}\
&\approx\frac{125\times 3.14}{12}\
&=\frac{392.5}{12}\
&\approx 32.71
\end{align*}
$$

# Answer:
$32.71$

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Question

Explanation:

Step1: Recall the formula for the area of a sector

Step2: Substitute the given values into the formula

Answer: