SOLUTION: The diameter of a sphere is increased by 3 times. By what factor does its volume increase? By what factor does its surface area increase?

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Question 1066744: The diameter of a sphere is increased by 3 times. By what factor does its volume increase? By what factor does its surface area increase?
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The diameter of a sphere is increased by 3 times. By what factor does its volume increase? By what factor does its surface area increase?
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"increased by 3 times" ??
3 times the diameter?
or the original + 3 times --> 4 times the diameter?
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Vol is a function of the cube of the diameter.
SA is a function of the square of the diameter.

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
r for radius
d for diameter
r=d%2F2


For VOLUME v=%284%2F3%29pi%2A%28d%2F2%29%5E3

If diameter is increased three times, then new radius is 3d%2F2.
New volume, v%5Bn%5D=%284%2F3%29pi%2A%283d%2F2%29%5E3;

How do v%5Bn%5D and v compare?
How is the new volume changed? Ratio of v%5Bn%5D%2Fv?