Question

If the area of minor sector of a circle with radius 11.2 cm is 49.28 cm², find the measure of the arc.

Answer 1

Given:
Area of the sector = 49.28 cm²
Radius = 11.2 cm
We know:
Area of a sector = $\frac{\mathrm{\theta }}{360}\times \mathrm{\pi }{r}^2$
∴ Area of the sector = $\frac{\mathrm{\theta }}{360}\times \frac{22}{7}\times {\left(11.2\right)}^2$

⇒ 49.28 = $\frac{\mathrm{\theta }}{360}\times \frac{22}{7}\times {\left(11.2\right)}^2$

⇒ $\mathrm{\theta }$ = $\frac{49.28\times 7\times 360}{22\times 11.2\times 11.2}$

⇒ $\mathrm{\theta }$ = 45$°$

Thus, the measure of the arc is 45$°$.