posted by ASAP .
A cardboard box of 32in^3 volume with a square base and open top is to be constructed. What is the length of base that will minimize the surface area?
Surface area = s^2 + 4*s*h
using volume equation, h=32/s^2
SA= s^2 + 4*s*(32/s^2) = s^2 + 128/s
Take derivative dSA/ds and set equal to zero.
2s - 128/s^2 = 0
s^3 = 64
s = 4