Question

The area of sector of circle of radius 5cm is 5𝜋 cm2. Find the angle contained by the sector.

Answer 1

Area of sector = 5𝜋 cm².

Radius (r) = 5cm

Let 𝜃 = angle subtended at centre area of sector =${\displaystyle \frac{\theta }{{360}^{\circ }}\times \pi r^2}$

=${\displaystyle \frac{\theta }{360}\times \pi \times 5\times 5=\frac{5\pi \theta }{{72}^{\circ }}}$

=${\displaystyle \frac{5\pi \theta }{{72}^{\circ }}}$= 5𝜋

⇒ 𝜃 = 72°