Question : Two cylinders have their heights in the ratio 1 : 2 and their radii in the ratio 2 : 1. What is the ratio of their volumes?
Option 1: 3 : 1
Option 2: 1 : 3
Option 3: 2 : 1
Option 4: 1 : 2
Correct Answer: 2 : 1
Solution :
Let the radius and height of cylinder-1 and cylinder-2 be r, h, and R, H respectively
As given,
r : R = 2 : 1
h : H = 1 : 2
Volume of a cylinder = $\pi r^2 h$
Let their volumes be $V_1$ and $V_2$, So
Ratio, $\frac{V_1}{V_2} = \frac{\pi r^2 h}{\pi R^2 H}$
$⇒\frac{V_1}{V_2} = \frac{2^2\times 1}{1^2\times 2} = \frac{2}{1}$
$⇒V_1: V_2 = 2 : 1$
Hence, the correct answer is 2 : 1.
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