# calculus

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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 -

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 -

i got it wrong

• calculus -

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 -

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 -

THANK YOU

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