Question

The base radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 4. What is the ratio of their volumes?

The volume of the first cylinder is 720 cubic centimetres. What is the volume of the second?

Answer 1

Let the base radii of the first and second cylinders be 2x and 3x units respectively.

Let the heights of the first and second cylinders be 5y and 4y units respectively.

Base area of the first cylinder = πr²

= π(2x)² sq. units

= 4πx² sq. units

Volume of the first cylinder = Base area × Height

= 4πx² × 5y cubic units

= 20πx²y cubic units

Base area of the second cylinder = π(3x)² sq. units = 9πx² sq. units

Volume of the second cylinder = 9πx² × 4y cubic units = 36πx²y cubic units

Ratio of the volumes =

Therefore, the ratio of the volumes of the first cylinder to the second cylinder is 5:9.

Volume of the first cylinder = 720 cm³

∴ Volume of the second cylinder = × Volume of the second cylinder