A cylinder has a height that is 2 times as large as its radius. The lateral surface area of the cylinder is 36π square units. What is the length of the radius of the cylinder? Please show all work in order to receive credit.
Let R be the radius of the cylinder. Since the height is 2 times the radius, the height of the cylinder is 2R.
The lateral surface area of a cylinder is given by the formula 2πRh, where R is the radius and h is the height.
Given that the lateral surface area is 36π, we have:
2πR(2R) = 36π
4πR^2 = 36π
R^2 = 9
R = 3
Therefore, the length of the radius of the cylinder is 3 units.