Chapter 11, Problem 11CT

To determine

To Find: The area.

Answer to Problem 11CT

  $60\pi sq.units$

Explanation of Solution

Given: A sector of a circle with $radius=12,arclength=10\pi$

Given: $radius=12,arclength=10\pi$

First we need to find the measure of angle.

Thus

Using the formula fo arc length.

  $\begin{array}{l}A=\frac{x}{360}\cdot 2\pi r\\ 10\pi =\frac{x}{360}\cdot 2\pi (12)\\ \frac{10}{24}\cdot 360=x\\ x=150\end{array}$

Now area of sector.

  $\begin{array}{l}A=\frac{x}{360}\cdot \pi r^2\\ $ A=\frac{150}{360}\cdot \pi {(12)}^2$A=\frac{5}{12}\cdot 144\pi \\ A=60\pi sq.units\end{array}$