Question

The area of the shaded sector below is equal to 8 pie.Find the measure of the central angle (in degrees).

Answer 1

Given:

`\begin{gathered} Area\text{ of sector}=8\pi \\ r=8\text{ }in \end{gathered}`

To get the central angle, we use the formula for the area of a sector;

`A=(\theta)/(360)*\pi r^2`

Hence, substituting the given values into the formula,

`\begin{gathered} 8\pi=(\theta)/(360)*\pi*8^2 \\ 8\pi=(64\pi*\theta)/(360) \\ Cross\text{ multiplying,} \\ 64\pi\theta=360*8\pi \\ 64\pi\theta=2880\pi \\ \\ Dividing\text{ both sides by 64}\pi, \\ \theta=(2880\pi)/(64\pi) \\ \theta=45^0 \end{gathered}`

Therefore, the measure of the central angle of the shaded sector is 45 degrees.