Question

in a circle with center ooo, central angle aobaoba, o, b has a measure of \dfrac{5 \pi}{4} 4 5π ​ start fraction, 5, pi, divided by, 4, end fraction radians. the area of the sector formed by central angle aobaoba, o, b is what fraction of the area of the circle?

Answer 1

The central angle of $aoba$ is $\frac{5\pi}{4}$ out of a full circle of $2\pi$, which means it covers $\frac{5\pi}{4}\div 2\pi=\frac{5}{8}$ of the circle. Therefore, the area of the sector formed by the central angle is $\frac{5}{8}$ of the total area of the circle.

So the fraction of the area of the sector formed by the central angle $aoba$ to the area of the circle is $\boxed{\frac{5}{8}}$.