Mensuration (C10)

A right circular cylinder and a cone have equal bases and equal heights. If their curved surface areas are in the ratio 8 : 5, show that the ratio between radius of their bases to their height is 3 : 4.

Answer

Let r be the radii of bases of cylinder and cone and h be the height

Slant height of cone = √(r2 + h2)

∴ 2πrh / πr√(r2 + h2) = 8/5

h / √(r2 + h2) = 4/5

h2 / (r2 + h2) = 16/25

⇒ 25h2 = 16r2 + 16h2

⇒ 9h2 = 16r2

⇒ r2 / h2 = 9/16

r / h = 3/4