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

Options
a) 4 : 11
b) 15 : 4
c) 11 : 15
d) 13 : 11

Solution

As per question
Two cones are in the ratio of 2 : 5
r₁ = 2
r₂ = 5
Volumes are in the ratio of 3 : 5
$ (\frac{r_1}{r_2})^2 \times \frac{H_1}{H_2} = \frac{3}{5}$
$ (\frac{2}{5})^2 \times \frac{H_1}{H_2} = \frac{3}{5}$
$ \frac{4}{25} \times \frac{H_1}{H_2} = \frac{3}{5}$
$ \frac{H_1}{H_2} = \frac{3}{5} \times \frac{25}{4}$
$ \frac{H_1}{H_2} = \frac{15}{4}$

Answer: b) 15 : 4