Problem 662

Find the area A of the sector of a circle of radius 30 feet formed by the central angle \frac{1}{13}radian.


A central angle is an angle whose vertex is at center  of a circle.

The rays of a circle 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. We have the following theorem.


Area of a Sector

The area A of a sector of a circle of radius r formed by a central angle of \theta radians is

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


The  value of r in the formula is 30 feet.

The value of \theta in the formula is \frac{1}{13} radian.


A (area) = \frac{1}{2}.(30 feet)^{2}*\frac{1}{13}

= 34.615 feet^{2}.


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