Question

A box with a square base and open top must have a volume of 4,000 cm^3. Find the dimensions of the box that minimize the amount of material used.
sides of base cm
height cm

Answer 1

For sides of base I got 20cm and for height I got 10 cm? Anybody agree or disagree with me?

Answer 2

the volume
v = x^2 z = 4000, so z = 4000/x^2

the area is

a = x^2 + 4xz = x^2 + 16000/x
da/dx = 2x - 16000/x^2
da/dx=0 when

2x - 16000/x^2 = 0
x^3 = 8000
x = 20

So the box is 20x20x10 cm

Answer 3

Same as what I got