Question

The ratios of the respective heights and the respective radii of two cylinders are $1:2$ and $2:1$ respectively. Then their respective volumes are in the ratio.

• A. $4:1$
• B. $1:4$
• C. $2:1$
• D. $1:2$

Answer 1

Answer: (C)

$2:1$

Consider the given ratios.

$h_1:h_2=1:2$

$r_1:r_2=2:1$

We know that the volume of the cylinder

$V=\pi r^{2}h$

So, the ratio of volumes of two cylinders

$\frac{V_1}{V_2}=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}$

$\frac{V_1}{V_2}={\left(\frac{r_1}{r_2}\right)}^2\times \frac{h_1}{h_2}$

$\frac{V_1}{V_2}={\left(\frac{2}{1}\right)}^2\times \frac{1}{2}$

$\frac{V_1}{V_2}=\left(\frac{4}{1}\right)\times \frac{1}{2}$

$\frac{V_1}{V_2}=\frac{2}{1}$

$V_1:V_2=2:1$

Hence, this is the answer.