The area is what fraction of the circle?

Question

In a circle with center P, central angle MPN has a measure of 3pi/4 radians. The area of the sector formed by the central angle MPN is what fraction of the circle?

Answer 1

π radians is 1/2 of the circle

3π/4 radians is (3/4)(1/2) = 3/8

Answer 2

one easy way is to convert 3pi/4 to degrees (135) and take the ratio of that sector's central angle to 360 degrees; that's 3/8.