Question

Find the radius of the sector which is making an angle of ${60}^{\circ }$ and has an area of 924 ${cm}^2$. (use $\pi$ = $\frac{22}{7}$)

• A. 42 cm
• B. 32 cm
• C. 52 cm
• D. 50 cm

Answer 1

The correct option is A 42 cm

Area of sector = $\frac{x^{\circ }}{{360}^{\circ }}$ $\times$ $\pi$$\times$ $r^2$

Given: $x={60}^{\circ }$ and Area = 924 ${cm}^2$
so, 924 = $\frac{{60}^{\circ }}{{360}^{\circ }}$ $\times$ $\frac{22}{7}$$\times$ $r^2$
$\Rightarrow$ $r^2$ = 924 $\times$ $\frac{{360}^{\circ }}{{60}^{\circ }}$$\times$ $\frac{7}{22}$ = 1764
$\Rightarrow$ $r$ = 42 cm