Two right circular cones, C 1 and C 2 , have their heights in the ratio 2 : 1 and radii in the ratio 1 : 2. The ratio of their volumes is:

Given,

Ratio of heights ($h_1 : h_2$) = 2 : 1

Ratio of radii ($r_1 : r_2$) = 1 : 2

By formula,

Volume of cone = $\frac{1}{3} \pi r^2 h$

$$\begin{aligned}\therefore \frac{V_1}{V_2} = \frac{\frac{1}{3} \pi r_1^2 h_1}{\frac{1}{3} \pi r_2^2 h_2} \\[1em] = \frac{r_1^2 h_1}{r_2^2 h_2} \\[1em] = \frac{1^2 \times 2}{2^2 \times 1} \\[1em] = \frac{2}{4} \\[1em] = \frac{1}{2}.\end{aligned}$$

Ratio of volumes = 1 : 2.

Hence, option 2 is the correct option.