Question

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

• A. $r_2^2:r_1^2$
• B. $2r_1^2:r_2^2$
• C. $25:9$
• D. $9:25$

Answer 1

The correct option is D $9:25$

Let $r_{1}and{r}_2$ be the radii of two cones and $V_{1}and{V}_2$ their volumes.
Let h be the height of the two cones, then
$V_1=\frac{1}{3}{r}_1^{2}and{V}_2=\frac{1}{3}{r}_2^{2}h$
$\frac{v_1}{v_2}=\frac{\frac{1}{3}\pi r_1^{2}h}{\frac{1}{3}\pi r_2^{2}h}=\frac{r_1^2}{r_2^2}=\frac{9}{25}(\because r_1:r_2=3:5)$