Question

Two right circular solid cylinder have radii in the ratio $3:5$ and heights in the ratio $2:3$. Find the ratio between their volumes.

• A. $6:25$
• B. $2:9$
• C. $6:13$
• D. $3:17$

Answer 1

The correct option is A $6:25$

Let, radius of first cylinder $=r_1=3x$
and radius of second cylinder $=r_2=5x$

Also, let height of first cylinder $=h_1=2y$
and height of second cylinder $=h_2=3y$

Volume of first cylinder $=V_1=\pi (r_1{)}^2{h}_1$

$=\pi (3x{)}^{2}2y$

$=18x^{2}y\pi$

Volume of second cylinder $=V_2=\pi (r_2{)}^2{h}_2$

$=\pi (5x{)}^{2}3y$

$=75x^{2}y\pi$

$\therefore \frac{V_1}{V_2}=\frac{18x^{2}y\pi }{75x^{2}y\pi }$

$=\frac{18}{75}=\frac{6}{25}$

Ratio of their volumes $=6:25$
Option A is correct.