Question

In a circle with center O, central angle $AOB$ has a measure of $\frac{5\pi }{4}$ radians. The area of the sector formed by central angle $AOB$ is what fraction of the area of the circle?

• A. $\frac{5}{8}$
• B. $\frac{8}{5}$
• C. $\frac{16}{5}$
• D. $\frac{4}{5}$

Answer 1

The correct option is A $\frac{5}{8}$

We know that the central angle of a circle is $2\pi$
Portion of the circle occupied by AOB $=\frac{\frac{5\pi }{4}}{2\pi }=\frac{5}{8}$