Question

The volume of a solid cylinder and a solid cone are same. If their radii are also same, the ratio between the heights of cylinder and cone is:

Options

• 3 : 1

• 2 : 3

• 1 : 3

• 3 : 2

Answer 1

1 : 3

Explanation:

Radii of cylinder = Radii of cone = r (let)

Let height of cylinder be h₁ and height of cone be h₂.

Given,

Volume of a solid cylinder and a solid cone are same.

\[\Rightarrow \pi r^2 h_1 = \frac{1}{3}\, \pi r^2 h_2\]

\[\Rightarrow h_1 = \frac{1}{3}\, h_2\]

\[\Rightarrow \frac{h_1}{h_2} = \frac{1}{3}\]

⇒ h₁ : h₂ = 1 : 3