calculus optimaization question please help NOW!?

Question

if 1200 cm^2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

The correct answer is 4000cm^3. show all work thanks

Answer 1

I'll leave you to do some of it.

Let the length of the base be x cm, the height h cm.

The total area of base and sides is
x^2 + 4*h, and since we are told this is 1200 sq cm, we write
x^2 + 4h = 1200, which allows us to express h in terms of x. [You can do that.]

Now volume
V = (x^2)*h, and if you replace h by the expression you just found, you have V as a function of x only. I expect you've already done the mechanics of differentiation and finding max val, so I'll leave you to finish it yourself or copy from others who will post the complete working here or you can email [e-mail]

Answer 2

1200/6=200 (because there are 6 faces)

A(x) = 6x^2 (its a square, all sides equal)

(Crossection multiply by length = volume)
V(x) = 200*200 = 40000cm^3 (This is current volume and the maximum volume)

Note: Usual calculus method will not work here because there is only one turning point in the volume(x) graph.

Correct answer is 40000cm^3

Answer 3

1200 / 5 = 240 cm^2 per side of box. Because its open top.

so 15.495 x 15.495 x 15.495 = 3720 cm^3 maximum volume