Question

The radius of two cylinders are in the ratio $2:3$ and their heights are in the ratio $3:5$. Find the ratio of their volumes.

• A. $\frac{2}{3}$
• B. $\frac{3}{5}$
• C. $\frac{4}{15}$
• D. $\frac{3}{2}$

Answer 1

Answer: (C)

$\frac{4}{15}$

For Cylinder $1$:

$r_1=2x$

$h_1=3y$

For Cylinder $2$:

$r_2=3x$

$h_2=5y$

Ratio of the volumes$=\frac{\pi r_1^2{h}_1}{\pi r_2^2{h}_2}$

$=\frac{\pi \times 4x^2\times 3y}{\pi \times 9x^2\times 5y}$

$\Rightarrow \frac{4}{15}$