Calculus

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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?

• Calculus -

Volume=s^2*h=32

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

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