Question

Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°.

Answer 1

Consider a sector OACB of a circle, where the angle subtended at the center O is 60°.

The formula for the area of a sector with angle θ is: \( \frac{θ }{ 360 ^{\degree}} \times πr^2\)

For sector OACB, the area is calculated as: \( \frac{60^{\degree}}{360^{\degree}} \times \frac{22}{7} \times (6)^2\)

This simplifies to: \( \frac{1}{6 }\times \frac{22}{7} \times6 \times 6 = \frac{132}{ 7} cm^2\)

Therefore, the area of the sector is \(\frac{132}{ 7} cm^2\).