Question

An arc of length 5pi cm and the sector it bounds has an arc of 20pi cm.Find the radius of the circle.

Answer 1

Area of sector = angle in radians * r^2 * 0.5
20 \pi = angle in radians * r^2 * 0.5
40 \pi / r^2 = angle in radians

Length of minor arc = angle in radians * radius (r)
5 \pi / radius = angle in radians

So....

40 \pi / radius^2 = 5 \pi / radius

5 \pi radius^2 / radius = 40 \pi

5 \pi radius = 40 \pi

5(pi)r = 40pi (which you got)
r= 40pi/5pi
pis cancel out, r=8