50
An arc of length $22$ cm subtends an angle of $60^{\circ}$ at the centre of the circle. Find the area of the sector of the circle made by the arc.
Show SolutionHide Solution↓
Length of arc = $22$ cm ($\frac{1}{2}$ Mark)
Central angle = $60^{\circ}$
Length of arc = $\frac{2\pi r \theta}{360}$ ($\frac{1}{2}$ Mark)
$22 = \frac{60}{360} \times 2 \times \frac{22}{7} \times r$ ($\frac{1}{2}$ Mark)
$r = 21$ cm
Area of sector = $\frac{60}{360} \times \frac{22}{7} \times (21)^2$ ($\frac{1}{2}$ Mark)
$= 231$ cm$^2$
Central angle = $60^{\circ}$
Length of arc = $\frac{2\pi r \theta}{360}$ ($\frac{1}{2}$ Mark)
$22 = \frac{60}{360} \times 2 \times \frac{22}{7} \times r$ ($\frac{1}{2}$ Mark)
$r = 21$ cm
Area of sector = $\frac{60}{360} \times \frac{22}{7} \times (21)^2$ ($\frac{1}{2}$ Mark)
$= 231$ cm$^2$