SOLUTION: how many times does the volume of a sphere increases if the radius is 1) double 2)half

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Question 321274: how many times does the volume of a sphere increases if the radius is
1) double 2)half
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The volume of a sphere is given by:
V+=+%284%2F3%29pi%2Ar%5E3 Where r = radius.
1) Let's what happens when you double the radius:
V+=+%284%2F3%29pi%2A%282r%29%5E3
V+=+%284%2F3%29pi%2A%288r%5E3%29 Move the 8 to the front.
V+=+8%284%2F3%29pi%2Ar%5E3...and you can see that the volume V is 8 times the original volume.
2) ...and if we divide the radius by 2...
V+=+%284%2F3%29pi%28r%2F2%29%5E3
V+=+%284%2F3%29pi%28r%5E3%2F8%29 or...
V+=+%281%2F8%29%284%2F3%29pi%2Ar%5E3 ...so the volume is decreased by a factor of 8.