Question

I really need help on this problem.

A sector has area of 15 in^2 and central angle of 0.2 radians. Find the radius of the circle and arc length of the sector

Answer 1

area of whole circle /15 = 2π/.2
area of whole circle = 30π/.2 = 150π

then πr^2 = 150π
r^2 = 150
r = √150 = 5√6

arclength = rØ = 5√6(.2) = √6

or if you don't know that formula .....
arc /(2π(5√6) = .2/(2π)
arc = 2π(5√6)(.2)/(2π) = √6