The radii of the base of a cylinder and a cone are in the ratio 3:4. If they have their height in the ratio 2:3, the ratio between their volumes is:

Given: The radii of the base of a cylinder and a cone are in the ratio 3:4.

Heights of the base of a cylinder and a cone are in the ratio 2:3.

Volume of cylinder is: πr²h (here r and h are radius and height of the cylinder respectively)

Volume of cylinder is: πr²h

Let V₁ be the volume of first cylinder

∴ V₁ = π(r₁)²h₁

Let V₂ be the volume of the cone.

∴ V₂ = π(r₂)²h₂

∴ V₁ : V₂ = π(r₁)²h₁ : π(r₂)²h₂

⇒ V₁ : V₂ = π × (3)² × 2 : × π × (4)² × 3

⇒ V₁ : V₂ = 18π : × 48π = 18:16 = 9:8

∴ V₁ : V₂ = 9:8

That is the ratio of their volume is 9:8.