SAT Mathematics Practice Test 3

A complete rotation around a point is 360° or 2π radians.
Since the central angle AOB has measure $5\frac{\mathit{\pi }}{4}$ radians,
it represent $\frac{\frac{5\mathit{\pi }}{4}}{2\mathit{\pi }}=\frac{5}{8}$ of a complete rotation around point O.
Therefore, the sector formed by central angle AOB has area equal to $\frac{5}{8}$ the area of the entire circle.
Either the fraction $\frac{5}{8}$ or its decimal equivalent, .625, may be gridded as the correct answer.