Find Rational Function S

[mathdad]

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 5000 cubic inches. Find a rational function S in terms of x for the surface area of the box if V = length times width times height, where length = x, width = x and height = y.

Let me see how far I can go.

I need to find S(x).

So, x = width and length,
y = height.

V is volume.

V = width * length * height

V = x * x * y

Let V = 5000

I know have 5000 = yx^2.

Surface area (since it is a closed box) must be:

SA = 2(area of the base) + (perimeter of the base)(height).

SA = 2x^2 + 4xy

Question:

Must I solve 5000 = yx^2 for y and replace y in SA? The rational function must be in terms of x.

 

[Dr.Peterson]

Yes.

The work you are asked to do here is the first part of the work for a common type of calculus problem.