A circle has center O. A shaded sector of the circle has a central angle of 90 degrees.

Question

The circle has center O

, and the central angle of the shaded sector measures 90 degrees

. The area of the shaded sector is what fraction of the area of the circle?
(The number of degrees of arc in a circle is 360

.)

Answer 1

Since the central angle of the shaded sector is 90 degrees, the shaded sector makes up 90/360 = 1/4 of the entire circle.

Therefore, the area of the shaded sector is 1/4 of the area of the entire circle.

So, the shaded sector is 1/4 or 25% of the area of the circle.