Question

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

Answer 1

Solution:

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;

$A=\frac{\theta}{360}\times\pi r^2$

Hence, substituting the given values into the formula,

$\begin{gathered} 8\pi=\frac{\theta}{360}\times\pi\times8^2 \\ 8\pi=\frac{64\pi\times\theta}{360} \\ Cross\text{ multiplying,} \\ 64\pi\theta=360\times8\pi \\ 64\pi\theta=2880\pi \\ \\ Dividing\text{ both sides by 64}\pi, \\ \theta=\frac{2880\pi}{64\pi} \\ \theta=45^0 \end{gathered}$

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