Posted by **kwack** on Tuesday, September 7, 2010 at 3:13am.

If 2100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Volume = cubic centimeters.

- calculus -
**drwls**, Tuesday, September 7, 2010 at 8:26am
Let x = side width and y = height.

Area = x^2 + 4xy = 2100

y = (2100 -x^2)/(4x) = (525/x) - (x/4)

Volume = y*x^2 = 525x -(x^3/4)

dV/dx = 0 = 525 - (3/4)x^2

x = sqrt 733.3 = 26.45 cm

y = 13.24 cm

max volume = 14,410 cm^3

- calculus -
**kwack**, Tuesday, September 7, 2010 at 5:54pm
i got it wrong

- calculus -
**drwls**, Tuesday, September 7, 2010 at 11:54pm
You did or I did?

You need to specify if all material gets used. If not, and you are just cutting square corners off the original piece, folding up tabs and throwing away the squares, then you need to say if the original material is a square or not.

- calculus -
**drwls**, Wednesday, September 8, 2010 at 1:01am
There are a few math errors in my answer.

x = sqrt700 = 26.45 cm

y = 525/x -x/4 = 13.24 cm

max volume = y*x^2 = 9263 cm^3

- calculus -
**HELLLLLPPPPP**, Wednesday, September 8, 2010 at 1:39am
THANK YOU

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