Question

If skating track of length 55 m, as shown in figure, subtends ${150}^o$ angle at center of circle, find radius of circle.

• A. 11 m
• B. 14 m
• C. 21 m
• D. 42 m

Answer 1

The correct option is C 21 m

Given length of the arc = 55 m , angle subtended = 150°
Length of arc = $\frac{Angle}{{360}^o}$$\times$2$\pi$r
Length of track = $\frac{{150}^o}{{360}^o}$$\times$2$\times$$\frac{22}{7}$$\times$r
55 = $\frac{5}{12}$$\times$2$\times$$\frac{22}{7}$$\times$r
$\frac{55\times 12\times 7}{5\times 2\times 22}$ = r

r = 21 m
Radius of circle whose track is part is 21 m.