Question

The radii of the bases of a cylinder and cone are in the ratio $3:4$ and their heights are in the ratio $2:3$ then their volumes are in the ratio is

• A. $9:8$
• B. $8:9$
• C. $3:4$
• D. $4:3$

Answer 1

The correct option is A $9:8$

Volume of a cone $=\frac{1}{3}\pi r_1^2{h}_1$

where $r_1$ is the radius of the cone

$h_1$ is the height of the cone.

Volume of a cylinder $=\pi r_2^2{h}_2$

where $r_2$ is the radius of the cylinder.

$h_2$ is the height of the cylinder

So, as $\frac{r_2}{r_1}=\frac{3}{4}$, $\frac{h_2}{h_1}=\frac{2}{3}$

So, ratio $=\frac{volumeofcylinder}{volumeofcone}$

$=\frac{\pi r_2^2{h}_2}{\frac{1}{3}\pi r_1^2{h}_1}$

$=3{\left(\frac{r_2}{r_1}\right)}^2\left(\frac{h_2}{h_1}\right)$

$=3{\left(\frac{3}{4}\right)}^2\left(\frac{2}{3}\right)$

$=3\times \frac{9}{16}\times \frac{2}{3}$

$=\frac{9}{8}$

$\therefore$ Ratio is $9:8$.