Question

Suppose a cone and a cylinder have the same radius and that the slant height l of the cone is the same as the height h of the cylinder. Find the ratio of the cone's surface area to the cylinder's surface area.

Area of cone: S = πrl + πr^2

Area of cylinder: S = 2πrh + 2πr^2

Answer 1

just divide the two, as you would do with any ratio:

(πrl + πr^2) / (2πrh + 2πr^2)

πr(l+r) / 2πr(h+r)
= (l+r) / 2(h+r)