Question

The base radii of two cylinders of the same height are in the ratio 3 : 4. What is the ratio of their volumes?

Answer 1

Let the base radii of the first and second cylinders be 3x and 4x units respectively.

Let the height of the cylinders be h units.

Base area of the first cylinder = πr²

= π(3x)² sq. units

= 9πx² sq. units

Volume of the first cylinder = Base area × Height

= 9πx²h cubic units

Base area of the second cylinder = π(4x)² = 16πx² sq. units

Volume of the second cylinder = 16πx²h cubic units

Ratio of the volumes =

Therefore, the ratio of the volumes of the first cylinder to the second cylinder is 9:16.