A right circular cylinder and a cone have equal bases and equal heights

• 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