# If the ratio of radii of two cylinders is 2 ∶ 3 and the ratio of their heights is 5 ∶ 3, then the ratio of their volumes is

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## Options:

1. 20 ∶ 27

2. 21 ∶ 25

3. 27 ∶ 25

4. None of the above

### Correct Answer: Option 1 (Solution Below)

This question was previously asked in

Official Paper 5: Tripura TET 2018 Paper 2 (Maths & Science)

## Solution:

Given:

The ratio of radii of two cylinders is 2 ∶ 3 and the ratio of their heights is 5 ∶ 3

Formula used:

The volume of the cylinder = π r2 h

Here, r is the radius and h is the height of the cylinder

Calculation:

Let the radius be 2x and 3x respectively

And, let the height be 5y and 3y respectively

⇒ The ratio of the volume $$= {{r^2\times h} \over R^2\times H}$$

⇒ $${{2x^2\times 5y} \over 3x^2\times 3y}$$ = 20/27

∴ The ratio of their volumes is 20 ∶ 27
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