Chapter 11.6, Problem 12WE

To determine

To Find: The radius.

Answer to Problem 12WE

  $r=2$

Explanation of Solution

Given: $\angle AOB=315,A=\frac{7}{2}\pi$

Given: $\angle AOB=315,A=\frac{7}{2}\pi$

Area of the sector.

  $\begin{array}{l}A=\frac{x}{360}(\pi r^2)\\ \frac{7}{2}\pi =\frac{315}{360}(\pi r^2)\\ \frac{7}{2}\pi =\frac{7}{8}(\pi r^2)\\ r^2=4\\ r=2\end{array}$

Hence, $r=6$