If the radius of a sphere is doubled then the volume of a sphere becomes

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Doubled

Six times

Four times

Eight times

answer is D.

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Detailed Solution

Given that the radius of a sphere is doubled.
Let the radius of the sphere is r. The formula for the volume of sphere is given by,
Volume of a sphere

= \frac{4}{3} π r^{3}

, where

r

is the radius.
If the radius of the sphere is doubled then the radius is 2r. So, the volume of new sphere =

\frac{4}{3} π (2 r)^{3} = \frac{4}{3} \times 8 r^{3}

Thus, the ratio of new and old sphere=

\frac{\frac{4}{3} \times 8 r^{3}}{\frac{4}{3} \times r^{3}} = \frac{8}{1}

Therefore, if the radius of a sphere is doubled then the volume of a sphere becomes 8 times.
Hence, option (4) is correct.

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