Pre-calculus help!!?

Question

This may be hard to understand without the pic, but here goes.

The figure shows an open box with a square base and a partition down the middle. The box is to have a volume of 400 cubic inches. Express the amount of material needed to construct the box ,A, as a function of the length of a side of its square base, x.

The box looks like a shoe box with a partition down the center. The length and width are x, and the height is y.

Help, thanks.

Answer 1

The area of base is x^2
The height is 400/x^2
The 4 sides and the partition each have area = 400/x
So total area = x^2 + 5*400/x= x^2 + 2000/x

Answer 2

okay, basically you want a function of the material needed to make the box (in area) in terms of the length of base (in this case, x)

Volume, V= 400

The volume can also be expressed in terms of width x length x height. So;

V= x.x.y or V= yx²

Therefore, yx² = 400
y = 400/x² -------------------------- (eq. 1)

Now, consider the surface area of the box (the amount of material)

Surface area, A = 4 sides of box + the base + the partition
Therefore,
A = (4)xy + x² + xy

giving

A = 5xy + x² -------------------------------------------- (eq. 2)

now simply replace y in (eq. 2) with (eq.1) above and you'll get;

A = 2000/x + x²

Done! you have just described the surface area in terms of the box's base length, x. :D all the best bro.