## Problem 1111

*Find the central angle **θ** 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 (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. *

*Area of a sector*

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

*A = r ^{2} *

*θ*

*Solving for **θ** given **θ** = .*

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

*θ** =*

*=*

* 0.347*

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

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