Question

The radii of two right circular cylinders are in the ratio $2:3$. Find the ratio of their volumes if their heights are in the ratio $5:3$.

• A. $V_1:V_2=20:27$
• B. $V_1:V_2=26:27$
• C. $V_1:V_2=21:27$
• D. None of these

Answer 1

The correct option is A $V_1:V_2=20:27$

We have,

$\frac{r_1}{r_2}=\frac{2}{3}$

$\frac{h_1}{h_2}=\frac{5}{3}$

We know that the volume of the cylinder

$=\pi r^{2}h$

So, the ratio of the volume of cylinders

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

$={\left(\frac{2}{3}\right)}^2\times \frac{5}{3}$

$=\left(\frac{4}{9}\right)\times \frac{5}{3}$

$=\frac{20}{27}$

Hence, this is the answer.