Question

circle p with a radius of 4 centimeters is shown. which expression represents the area of the shaded sector of circle p? a. $\frac{20pi}{18}$ square centimeters b. $\frac{20pi}{1}$ square centimeters c. $\frac{16pi}{3}$ square centimeters d. $\frac{50pi}{9}$ square centimeters

Explanation:

Step1: Find the central angle of the shaded sector

The sum of angles in a circle is 360°. The non - shaded angles are 95° and 120°. So the central angle of the shaded sector $\theta=360-(95 + 120)=145^{\circ}$.

Step2: 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 $r$ is the radius of the circle and $\theta$ is the central angle of the sector. Here, $r = 4$ cm.

Step3: Substitute the values into the formula

$A=\frac{145}{360}\times\pi\times4^{2}=\frac{145}{360}\times16\pi=\frac{145\times16\pi}{360}=\frac{58\pi}{9}$ square centimeters.

Answer:

D. $\frac{58\pi}{9}$ square centimeters