Question

the circle has center o. its radius is 8 ft, and the central angle a measures 50°. what is the area of the shaded region? give the exact answer in terms of π, and be sure to include the correct unit in your answer.

Explanation:

Step1: Recall sector - area formula

The formula for the area of a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta$ is the central - angle measure in degrees and $r$ is the radius of the circle.

Step2: Substitute given values

We are given that $r = 8$ ft and $\theta=50^{\circ}$. Substitute these values into the formula: $A=\frac{50^{\circ}}{360^{\circ}}\times\pi\times(8)^{2}$.

Step3: Simplify the expression

First, simplify $\frac{50}{360}=\frac{5}{36}$, and $(8)^{2}=64$. Then $A=\frac{5}{36}\times\pi\times64=\frac{320}{36}\pi=\frac{80}{9}\pi$ square feet.

Answer:

$\frac{80}{9}\pi$ ft²