A rectangular box with a square base of length x and height h is to have a volume of 20ft^3. The cost of the top and bottom of the box is 20 cents per square foot and the cost of the sides is 8 cents per square foot. Express the cost of the box in terms of:

Question

The variable x and h
The variable x only
The variable h only

Approximate the dimensions of the box that will minimize the cost

Answer 1

clearly
x^2 h = 20 ---> h = 20/x^2 OR x = √(20/h)

so you have :
cost = base + 4 sides
= 20x^2 + 8(4xh)

to get the other two,
replace h with 20/x^2 to get it in terms of x

or

replace the x with √(20/h) to get it in terms of h