Question

A cardboard box of 32 in^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?

Answer 1

Step-by-step explattttttrttrtrtrnation:

Answer 2

volume = are base*height
32 = x^2*h --> h = 32/x^2

surface area = 4x(32/x^2) + x^2
SA = 128/x + x^2

SA' = -128/x^2 + 2x = 0
2x = 128/x^2
2x^3 = 128
x^3 = 64
x = 4

surface area minimized when length of base is 4 in.

hope this help