Problem 663

Find the central angle \theta 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  \theta radians is equal to the following.

 

 

A = \frac{1}{2}r^{2}\theta

 

Solving for \theta=\frac{2A}{r^{2}}. Substitute the values for A and r, and simplify.

\theta=\frac{2A}{r^{2}}

=\frac{2*21 square feet}{(11 feet)^{2}}

\approx 0.347 radians

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

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