Problem 1110

Find the area A of the sector of a radius 30 feet formed by the central angle \frac{1}{13} 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 = \frac{1}{2} r2 θ

The value of r in the formula is 30 feet.

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

Therefore,

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

= 34.615 feet2

 

 

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