A box with a square base and open top must have a volume of 237276 cm^3. We wish to find the dimensions of the box that minimize the amount of material used. Find a formula for the surface area of the box in terms of only x, the length of one side of the square base.[Hint: use the volume formula to express the height of the box in terms of x.]

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 237276 cubic centimetre. We want to find a formula for the surface area of the box in terms of only x, the length of one side of the square base.

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume,

Surface Area of the box = Base Area + Area of 4 sides

Substitute h derived above into A(x,h)

Therefore, a formula for the surface area of the box in terms of only x, the length of one side of the square base is:

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3