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  • Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60°.

Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60°.

Answers (1)

\left [ \frac{308-147\sqrt{3}}{3} \right ] 

Solution

Here    \theta=60^{\circ}

                        r=14 cm

Area of segment = \frac{\pi r^{2} \theta}{360}-\frac{1}{2}r^{2}\sin \theta

                       

                   \\=\frac{\frac{22}{7}\times 14 \times 14 \times 60}{360}-\frac{1}{2}\times 14 \times 14 \times \sin 60\\ =\frac{22 \times 28 \times 60}{360}-\frac{1}{2}\times 14 \times 14 \times \frac{\sqrt{3}}{2}\\ =\frac{308}{3}-49\sqrt{3}\\ =\frac{308-147\sqrt{3}}{3}cm^{2}

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infoexpert24

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