Question

Find the length of the arc which is part of a sector whose area is 77 $c{m}^2$ and the radius of the circle is 7 cm.

• A. 11 cm
• B. 22 cm
• C. 44 cm
• D. 66 cm

Answer 1

The correct option is B 22 cm

Area of sector = $\frac{angle}{{360}^o}$$\times$$\pi$$r^2$
77 = $\frac{angle}{{360}^o}$$\times$$\frac{22}{7}$$\times$$7^2$
77 = $\frac{angle}{{360}^o}$$\times$22$\times$7
$\frac{angle}{{360}^o}$ = $\frac{77}{22\times 7}$= $\frac{1}{2}$
angle = $\frac{{360}^o}{2}$ = ${180}^o$

Length of arc = $\frac{angle}{{360}^o}$$\times$2$\pi$r
= $\frac{{180}^o}{{360}^o}$$\times$2$\times$$\frac{22}{7}$$\times$7
= $\frac{1}{2}$$\times$2$\times$$\frac{22}{7}$$\times$7 = 22 cm