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February 18th, 2008, 05:37 PM   #1
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surface area to volume?

Hello,

Given that a box as a surface area of 14, how can I determine what the range of possible volumes would be? Or is there only one possible volume?

Thank you.
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February 19th, 2008, 04:50 AM   #2
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Re: surface area to volume?

Quote:
Originally Posted by captainglyde
Hello,

Given that a box as a surface area of 14, how can I determine what the range of possible volumes would be? Or is there only one possible volume?

Thank you.
Well, a cube has surface area 6s^2, so the maximum volume for a box would be sqrt(14/6)^3 ~= 3.56. As you flatten and lengthen the box (to keep SA constant) the volume decreases, so the volume can be any valid volume less than sqrt(14/6)^3. (If you allow zero volume, that can be achieved with 7 x 1 x 0, otherwise making it arbitrarily close will give an arbitrarily small volume.)
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February 19th, 2008, 08:30 AM   #3
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thanks a lot!
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