If the radius of a sphere is doubled, how many times its volume will be affected?

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2 times

4 times

6 times

8 times

answer is D.

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Detailed Solution

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

= 43 π r 3

, where r is the radius. According to given condition, the new radius will be r' = 2r. So, the new volume:

⇒ 43 π (2 r) 3 ⇒ 43 π × 8 r 3 ⇒ 8 43 π r 3

Therefore, if the radius of a sphere is doubled, 8 times its volume will be affected.
Hence, option (4) is correct.

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