Question

The radii of two cylinders are in the ratio $2:3$ and their curved surface areas are in the ratio $5:3$. What is the ratio of their volumes?

• A. $20:27$
• B. $10:9$
• C. $9:10$
• D. $27:20$

Answer 1

The correct option is B $10:9$

Given, ratio of two cylinders is $2:3$.

Thus $r,2x,r_2=3x$
Also given $\frac{{\text{CSA}}_1}{{\text{CSA}}_2}=\frac{2\pi r_1{h}_1}{\pi r_2{h}_2}=\frac{2x{h}_1}{3x{h}_2}=\frac{5}{3}$
$\Rightarrow \frac{h_1}{h_2}=\frac{5}{3}\times \frac{3}{2}=\frac{5}{2}$
Therefore, $\frac{V_1}{V_2}=\frac{\pi \times 2x\times 2x\times 5h}{\pi \times 3x\times 3x\times 2h}=\frac{20}{18}=\frac{10}{9}$