Thread: Find a Function

United States Service has contracted you to design a closed box with a square base that has a volume of 5000 cubic inches. Find a function for a surface area of the box.

Given Data:

height of box = y

width of box = x

length of box = x

Surface area is:

Area of bottom + area of top + area of all 4 sides.

As the base is square, the areas of the top and bottom are both x^2.

The area of each side is xy.

So the total surface area is 2x^2 + 4xy = 2x (x + 2y).

Now we can work out what the side y is in terms of x, because we know that the volume is 5000.

So we know that x times x times y = 5000, or that y = 5000/(x^2).

So we can plug this expression for y into the one for surface area:

Surface area = 2x (x + 2 (5000/(x^2))


A reasonable question to ask next is to find the value of x which makes the surface area a minimum - but only if you've done calculus.

Another great reply. I am learning so much on this website.

Great job guys!