Question

The base radii of two circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes are ______.

Options

• 9 : 25

• 5 : 3

• 9 : 5

• 3 : 25

Answer 1

The base radii of two circular cones of the same height are in the ratio 3 : 5. The ratio of their volumes are 9 : 25.

Explanation:

Let r₁ = 3x; r₂ = 5x; and h₁ = h₂ = h

`therefore  "Volume of 1st cylinder"/"Volume of 2nd cylinder" = (pi"r"_1^2"h"_1)/(pi"r"_1^2"h"_2)`

`= (9x^2"h")/(25x^2"h") = 9/25`

∴ Required ratio = 9 : 25