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If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second?

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2 : 8

1 : 2

1 : 3

1 : 8

answer is D.

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Detailed Solution

Given that the radius of a sphere is doubled.
Consider the radius to be

r

.
If the radius is doubled the new radius will be

2 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.
Therefore,
Ratio of volumes

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

= r^{3} : 8 r^{3}

= 1 : 8

Therefore, the ratio of volumes is

1 : 8

.
Hence option (4) is correct.

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