What is the area of a sector whose central angle is ninety degrees and has a radius of ten inches?

Well a circle has 360 degrees so a sector of 90 degrees has an area equal to 90/360 (or 1/4) of a circle with the equivalent radius.

The area of a circle is defined as PI*Radius^2 so the area of a 90 degree sector will be 1/4*PI*Radius^2.

The area will be 1/4*3.14*10^2 or 78.5 in^2.