Two right circular cones of equal volumes have their heights in the ratio 4 : 9. What is the ratio of the radii of their bases, the cones coming in the same order as that in which the ratio of their heights is given?

3 : 2

We know that,

Volume of a cone = \(\frac{1}{3}\)πr²h

Ratio of the heights of the cones =  4 ∶ 9.

Let the radius of the two cones = m and n

Also, let the heights of the cones be 4a and 9a

According to the question,

\(\frac{1}{3}\)π × m² × 4a = \(\frac{1}{3}\)π × n² × 9a

= 4m² = 9n²

= \(\frac{m}{n}\) = \(\frac{3}{2}\)

Ratio of radii = 3 : 2