## Problem 1110

*Find the area A of the sector of a radius 30 feet formed by the central angle radian.*

*Solution:-*

*A central angle is an angle whose vertex is at the center of a circle. The rays of a central angle subtend (intersect) an arc on the circle. The part of the circle between the rays of the angle and the arc subtended is called a sector. We have the following theorem.*

*Area of a sector*

*The area A of sector of a circle of radius r formed by a central angle of **θ** radians is *

*A = r ^{2} *

*θ*

*The value of r in the formula is 30 feet.*

*The value of **θ** in the formula is radian.*

*Therefore,*

*A (area) = *(30 feet) ^{2 }* *

*= 34.615 feet ^{2}*