Test 3 Section 4 #34

Remember that circle problems are often ratio problems, and this is definitely one of those cases. Generally, we can say that \dfrac{A_{\text{sector}}}{A_{\text{circle}}}=\dfrac{\text{central angle measure}}{360^\circ\text{ or }2\pi}.

Since we’re given the central angle in radians and no other information, we just need to figure out the ratio of the central angle to 2\pi.

    \begin{align*}\dfrac{\left(\dfrac{5\pi}{4}\right)}{2\pi}=\dfrac{5\pi}{8\pi}=\dfrac{5}{8}\end{align*}

You can either grid in that fraction or its decimal equivalent: .625.