A football tube in the form of a sphere is inflated so that it radius increases in the ratio 4:3 . Find the ratio in which the volume is increased.

The volume is increased in a ratio of 64/27

Explanation:

The Volume of a Sphere

The volume of a sphere of radius r is given by:

If the radius was changed to r', the new volume would be:

Dividing the latter equation by the first one:

Simplifying:

Or, equivalently:

Since r':r = 4:3, thus:

The volume is increased in a ratio of 64/27

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