SOLUTION: There is a box with a square base, and a volume of 32000cm^3, with an open top, what is the least material used, and what are the dimensions?

Question 30833: There is a box with a square base, and a volume of 32000cm^3, with an open top, what is the least material used, and what are the dimensions?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let a side of the square base = x
Let the height of the box = y
The volume, V =

The dimensions of the materials = 4*x*y for the sides
and x^2 for the base
M = materials

from above

find M'= MP the dirivative of M

set MP = 0 to find a minimum

multiply both sides by x^2

The base is 40X40 cm

The height is 20 cm

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