Calc derivatives - Minimum total surface area in a box of V = 160 ft2

[Dave_1420]

Hi everyone! I'm new to online math forums. I wonder if anyone can give me a hand on this - it would be greatly appreciated.

Thank you in advance!

Dave

Homework Statement

If a box with a square base and an open top is to have a volume of 160 cubic feet, find the dimensions of the box having the minimum total surface area. Use calculus to find the solution.

Homework Equations

If X are the sides of the base, and Y is the height of the box, what would be the formula to find surface? How can the minimum surface be calculated using derivative applications?

The Attempt at a Solution

Surface = minimum possible

 

[rock.freak667]

In terms of x and y, formulate an expression for the total outer surface area of the box.

 

[HallsofIvy]

If "x" is the length of a side of the square base, y is the height of the box, then the base is an "x by x" square and there are four sides that are "x by y" rectangles. Do you know how to find the area of squares and rectangles?