Question

If the area of the minor sector is 392. 5 sq. cm and the corresponding central angle is 72°, find the radius ($\mathrm{\pi }$ = 3.14)

Answer 1

Given:
Area of the sector = 392.5 cm²
Angle subtended at the centre, $\mathrm{\theta }$ = 72$°$
We know:
Area of a sector = $\frac{\mathrm{\theta }}{360}\times \mathrm{\pi }{r}^2$

Thus, we have:
Area of the sector = $\frac{72}{360}\times 3.14\times r^2$

⇒ 392.5 = $\frac{72}{360}\times 3.14\times r^2$

⇒ r² = $\frac{392.5\times 360}{3.14\times 72}$
⇒ r² = 625
⇒ r = $\sqrt{625}=25$ cm

Thus, the radius is 25 cm.