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 = \frac{1}{2} r2 θ

Solving for θ given θ = \frac{2A}{r^{2}}.

Substitute the values for A and r, and simplify.

θ =\frac{2A}{r^{2}}

=\frac{2 \cdot 21}{11}

\approx 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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