Question

2. What is the area of the shaded region below? Notice
that the angle is 120 degrees and the radius of the
circle is 8 inches.
8
120

Answer 1

Answer:

Approximately 67 square inches.

Step-by-step explanation:

The area of a circle is given by the formula:

$A=\pi r^2$

And the sector area of a circle is given by the formula:

$A=\frac{x\textdegree}{360\textdegree}(\pi r^2)$

Where x is the degree measurement of the sector.

We want to find the sector of the circle with a radius of 8. The degree measurement of the sector is 120. Therefore, plug 8 in for r and 120 for x:

$A=\frac{120\textdegree}{360\textdegree}(\pi(8)^2)$

The fraction reduces to 1/3. 8^2 is 64:

$A=\frac{1}{3}(64\pi)$

This is equivalent to:

$A=\frac{64}{3}\pi\\ A\approx67.0206 \text{ in}^2$