SOLUTION: Please, help me with this If each sides of a cube expands by r%. What is the approximate percentage change in its volume?

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Question 1027858: Please, help me with this
If each sides of a cube expands by r%. What is the approximate percentage change in its volume?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So assume that the side was originally, S.
Now it would be S%2Br%2F100
The volume originally was
V%5B1%5D=S%5E3
and the new volume,
V%5B2%5D=%28S%2Br%2F100%29%5E3}
V%5B2%5D=S%5E3%2B%283%2F100%29S%5E2r%2B%283%2F10000%29Sr%5E2%2B%281%2F1000000%29r%5E3
We can approximate by chopping off the last two terms,
V%5B2a%5D=S%5E3%2B%283%2F100%29S%5E2r
So then comparing,
V%5B2a%5D%2FV%5B1%5D=%28S%5E3%2B%283%2F100%29S%5E2r%29%2FS%5E3
V%5B2a%5D%2FV%5B1%5D=1%2B%283%2F100%29%28r%2FS%29
Multiply by 100 to make it a percentage,
V%5B2a%5D%2FV%5B1%5D=100%2B3%28r%2FS%29
Subtract 100 to find the percentage change,
PC=3%28r%2FS%29