Question

If the ratio of the base radii of a cylinder and a cone is 1 ∶ 2 and that of their heights is 2 ∶ 1, then what is the ratio of the volume of the cylinder to that of the cone?

• A. 2 ∶ 3
• B. 1 ∶ 1
• C. 2 ∶ 1
• D. 3 ∶ 2

Answer 1

Answer:

D. 3 ∶ 2

Solution:

Given:

Ratio of radii of base = 1 : 2

Ratio of heights = 2 : 1

Formula used:

Volume of cone = 1/3 πr²h

Volume of cylinder = πr²h

Calculation:

Let the radius of the cylinder and a cone are x and 2x, respectively.

The height of the cylinder and cone are 2y and y, respectively.

According to the question,

The volume of the cylinder = π × x² × 2y

⇒ 2πx²y 

The volume of the cone = (1/3) × π × 4x² × y

⇒ (4πx²y)/3

Required Ratio = 2πx2y : (4πx2y)/3

⇒ 3 ∶ 2 

∴ The ratio of the volume of the cylinder to that of the cone is 3 : 2.