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The area of the shaded sector is
8pi and the radius of the circle is 12 . What is the measure of the central angle?

$5$ . The area of the shaded sector is $8 \pi$ and the radius of the circle is $12$ . What is the measure of the central angle?

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Find the radius or diameter of a circle

Full solution

Q.

5

. The area of the shaded sector is

8 \pi

and the radius of the circle is

12

. What is the measure of the central angle?

Identify formula: Step $1$ : Identify the formula to use. $\newline$ The area of a sector of a circle is given by the formula $A = (\theta/360) \times \pi \times r^2$ , where $A$ is the area, $\theta$ is the central angle in degrees, and $r$ is the radius. $\newline$ Here, $A = 8\pi$ and $r = 12$ .
Plug in values: Step $2$ : Plug in the values and solve for $\theta$ . $8\pi = (\theta/360) * \pi * 12^2$ Simplify $12^2$ to $144$ . $8\pi = (\theta/360) * \pi * 144$
Cancel out $\pi$ : Step $3$ : Cancel out $\pi$ from both sides. $\newline$ $8 = (\frac{\theta}{360}) \times 144$
Solve for $\theta$ : Step $4$ : Solve for $\theta$ . $\frac{\theta}{360} = \frac{8}{144}$ Simplify $\frac{8}{144}$ to $\frac{1}{18}$ . $\frac{\theta}{360} = \frac{1}{18}$ Cross multiply to solve for $\theta$ . $\theta = \frac{1}{18} \times 360$ $\theta = 20$ degrees

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