Question

The radii of bases of the cylinder and a cone are in the ratio $3:4$ and their heights are in the ratio $2:3$. The ratio between the volume of the cylinder to that of the cone is:

• A. $8:9$
• B. $9:8$
• C. $5:7$
• D. $7:5$

Answer 1

The correct option is B $9:8$

Let $r$ be radius of base of the cylinder and $R$ be the radius of the base of the cone.

$\frac{r}{R}=\frac{3}{4}$

Let $h$ be the height of the cylinder and $H$ be the height of the cone.

$\frac{h}{H}=\frac{2}{3}$

$\therefore \frac{\text{Volume of cylinder}}{\text{Volume of cone}}=\frac{\pi r^{2}h}{\frac{1}{3}\pi R^{2}H}=3\times {\left(\frac{r}{R}\right)}^2\times \left(\frac{h}{H}\right)=3\times {\left(\frac{3}{4}\right)}^2\times \left(\frac{2}{3}\right)=\frac{9}{8}$