## Problem 663

Find the central angle which forms a sector of area 21 square feet of a circle of radius 11 feet.

Solution:-

A central angle is an angle whose vertex is at the center of a circle. The rays of a central angle subtend an arc on the circle. The part of the circle between the rays of the angle and the arc subtended is called a sector.

The area A of a sector of a circle of radius r formed by a central angle of radians is equal to the following.

A =

Solving for . Substitute the values for A and r, and simplify.

=

radians

Therefore , the central angle which from a sector a sector of area 21 square feet of a circle of radius 11 feet is = 0.347 radians.