My Math Forum surface area to volume?

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 February 18th, 2008, 05:37 PM #1 Newbie   Joined: Oct 2007 Posts: 10 Thanks: 0 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.
February 19th, 2008, 04:50 AM   #2
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Re: surface area to volume?

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 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.)

 February 19th, 2008, 08:30 AM #3 Newbie   Joined: Oct 2007 Posts: 10 Thanks: 0 thanks a lot!

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