A box with a square base and open top must have a volume of 32,000 cm3. Find the dimensions of the box that minimize the amount of material used.

Answer 1

V=32000=hs^2

h=32000/s^2

surface area=A=4hs+s^2

=128000/s+s^2

A'=2s-128000/s^2=0

2s^3=128000

s^3=64000

s=40 cm= side of square base

h=32000/1600=20 cm high