The volumes of two cones are in the ratio of 3 : 2 and their radii are in the ratio 3 : 4. The ratio of their heights is:

Correct option is A

Given:
Ratio of volumes of two cones = 3 : 2
Ratio of radii of the two cones = 3 : 4
Formula Used:
The volume of a cone is given by the formula:
V = $$\frac{1}{3}πr^2h$$​​
Solution:
Let the ratio of their radii is 3x: 4x
​$$V_1 = \frac 13 π(3x)^2h_1 = \frac 13 π(9x)^2h_1$$​​
​$$V_2 = \frac 13 π(4x)^2h_2 = \frac 13 π 16x^2h_2$$​​
Given that the ratio of volumes of the two cones is 3: 2,
​$$\frac{V_1}{V_2} = \frac{3}{2} \\\frac{ \frac 13 \pi 9x^2 h_1}{ \frac 13 \pi 16x^2 h_2} = \frac{3}{2} \\\frac{h_1}{h_2} = \frac{48x^2}{18x^2} \\\frac{h_1}{h_2} = \frac{8}{3}$$​​