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If the radius of the sphere is increased by 100100% then by what percentage will its volume increase?

Question

If the radius of the sphere is increased by 100100% then by what percentage will its volume increase?

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Solution

The volume of a sphere is given by the formula V = 4/3 * π * r³, where r is the radius of the sphere.

If the radius of the sphere is increased by 100%, it means the new radius is 2r.

The new volume V' of the sphere is then given by V' = 4/3 * π * (2r)³ = 4/3 * π * 8r³ = 8V.

This means the volume of the sphere has increased by 700%, because the new volume is 8 times the original volume, and 8 times is equivalent to an increase of 700%.

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