Question

The ratio of radii of two cylinders is $1:2$ and heights are in the ratio $2:3.$ The ratio of their volumes is

• A. 1:3
• B. 1:6
• C. 1:9
• D. 2:9

Answer 1

The correct option is B 1:6

Assume that ${}^{\prime }{r}^{\prime }$ and ${}^{\prime }{R}^{\prime }$ be the radii of the two cylinders and ${}^{\prime }{h}^{\prime }$ and ${}^{\prime }{H}^{\prime }$ be the height of the two cylinders respectively.

It is given that $\frac{r}{R}=\frac{1}{2}$ and $\frac{h}{H}=\frac{2}{3}$

We know that, the volume of a cylinder $=\pi r^{2}h$

Now, $\frac{v}{V}=\frac{\pi r^{2}h}{\pi R^{2}H}$

$\Rightarrow \frac{v}{V}=\left(\frac{r}{R}{)}^2\right(\frac{h}{H})$

$\Rightarrow \frac{v}{V}=\left(\frac{1}{2}{)}^2\right(\frac{2}{3})$

$\therefore \frac{v}{V}=\left(\frac{1}{4}\right)\left(\frac{2}{3}\right)=\frac{1}{6}$

Therefore, the ratio of their volume is $\frac{1}{6}.$