Question

Radius of a sector of a circle is 7 cm. If measure of arc of the sector is -

(1) 30^° (2) 210^° (3 ) three right angles;

find the area of the sector in each case.

Answer 1

Radius of the sector of the circle, r = 7 cm

(1)
Measure of arc of the sector = θ = 30º

∴ Area of the sector = $\frac{\theta }{360°}\times \mathrm{\pi }{r}^2=\frac{30°}{360°}\times \frac{22}{7}\times {\left(7\right)}^2$ = 12.83 cm²

(2)
Measure of arc of the sector = θ = 210º

∴ Area of the sector = $\frac{\theta }{360°}\times \mathrm{\pi }{r}^2=\frac{210°}{360°}\times \frac{22}{7}\times {\left(7\right)}^2$ = 89.83 cm²

(3)
Measure of arc of the sector = θ = 3 × 90º = 270º

∴ Area of the sector = $\frac{\theta }{360°}\times \mathrm{\pi }{r}^2=\frac{270°}{360°}\times \frac{22}{7}\times {\left(7\right)}^2$ = 115.5 cm²