Question

In a circle, an arc of length $4\pi \text{cm}$ subtends an angle of measure ${40}^{\circ }$ at the centre. Find the radius of the circle and the area of the sector corresponding to that arc.

Answer 1

Given:

$\theta ={40}^{\circ }$, arc length$=4\pi \text{cm}$

$\because$ Arc length $=\frac{\theta }{360}\times 2\pi r$

$⟹4\pi =\frac{40}{360}\times 2\pi r$

$⟹r=18\text{cm}$

$\because$ Area of sector $=\frac{\theta }{360}\times \pi r^2$

$⟹$ Area of sector $=\frac{40}{360}\times \pi \times {18}^2{\text{cm}}^2$

$⟹$ Area of sector $=36\pi {\text{cm}}^2$

$\therefore$ Area of sector $=113.04{\text{cm}}^2$.