Question : The ratio of the radii of two cylinders is $2:3$ and the ratio of their heights is $5:3$. The ratio of their volumes will be:
Option 1: $9:4$
Option 2: $20:27$
Option 3: $4:9$
Option 4: $27:20$
Correct Answer: $20:27$
Solution :
Given: The ratio of the radii of two cylinders is $2:3$ and the ratio of their heights is $5:3$.
Let the radii of the first cylinder = $2r$ units
So, the radii of the second cylinder = $3r$ units
Also, let their heights be $5h$ units and $3h$ units.
The ratio of their volume,
= $[\pi.(2r)^2.5h]:[\pi.(3r)^2.3h]$
= $[20\pi r^2h]:[27\pi r^2h]$
= $20:27$
Hence, the correct answer is $20:27$
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