A rectangular box with square base and top is to be made to contain 1250 cubic feet?

The box should be 10 x 10 x 12.5 feet for minimal cost

This is how I did it:
We know the box has a square base let x = length and y = height. Since length = width in this example we have:
x = length = width and y = height
We are given the volume of the box and volume is:
Vol = len * wid * height
From the question we have:
x * x * y = 1250
x^2*y = 1250
y = 1250/x^2
Now we have an equation relating length width and height
Now comes the fun part, figuring out the least cost. You have to find the surface area of each part of the box and multiply the price for each surface:
let SA = surface area to make our lives easier

cost = (cost of top) * (SA top) + (cost of bottom) * (SA of bottom) + (cost of side)*(SA of side)*(number of sides)
we know that:
SA top = x^2
SA bottom = x^2
SA side = x*y
Number of sides = 4
which gives:
cost = 35*x^2 + 15*x^2 + (4)*(20)*x*y
cost = 50x^2 + 80x*y
Now you need a way to have this function in on variable. Remeber that first equation? You have to sub that into the cost equation:
cost = 50x^2 +  10 0000 / x
Now you find the derivative of this function and make it equal to zero and solve for x:
cost ' = 100x - 10 0000/x^2
0 = 100x - 10 0000/x^2
gives:
x^3 = 1000
x = 10 is the only answer

Since y = 1250/x^2
y = 12.5

Now you know the dimensions:
The box should be 10 x 10 x 12.5 feet for minimal cost