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

Approximately 67 square inches.

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=(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=(120\textdegree)/(360\textdegree)(\pi(8)^2)`

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

`A=(1)/(3)(64\pi)`

This is equivalent to:

`A=(64)/(3)\pi\\ A\approx67.0206 \text{ in}^2`