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Question

If the radii and heights of two cylinders are in the ratio 1:2 and 2:1 respectively, then the ratio of their volumes is:

A
1:2
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B
2:1
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C
1:4
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D
4:1
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Solution

The correct option is A 1:2
Given, the ratio of the radii and heights of two cylinders are 1:2 and 2:1 respectively.

Let the radius of the first cylinder be x, then the radius of the second cylinder will be 2x.
Similarly, let the height of the first cylinder be 2y, then the radius of the second cylinder will be y.

We know that, Volume of a cylinder = π× (radius)2× height

Step 1: Volume of the first cylinder =π×(radius of the first cylinder)2×height of the first cylinder
=π×x2×2y
=2πx2y

Step 2: Volume of the second cylinder =π×(radius of the second cylinder)2×height of the second cylinder
=π×(2x)2×y
=4πx2y

Step 3: Ratio of the volumes
=Volume of the first cylinder : Volume of the second cylinder
=2πx2y:4πx2y
Divide both sides by 2πx2y
=2πx2y2πx2y:4πx2y2πx2y
=1:2

Hence, option (a.) is the correct choice.

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