# Calculus

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An open top box with a square base is to have a volume of exactly 500 cubic inches. Find the dimensions of the box that can be made with the smallest amount of materials.

• Calculus -

your turn to do this one
I will get you going ...

base: x by x
height : y
V = x^2 y
500 = x^2 y
y = 500/x^2

SA = base + 4 sides
= x^2 + 4xy
plug in y from above
differentiate
set that equal to zero and solve

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