An open rectangular box with a square base is to be made from 56 square feet of material. What dimensions will result in the box having the largest possible volume?

Question

pfenn1 · Answer

Each side of the box would be x^2.  There are only 5 sides to the box because there is no lid.  So$$5x^2 = 56$$Solve for x.

anonymous · Answer

How would that get me the largest volume though?

pfenn1 · Answer

The largest volume would be given by a cube.

anonymous · Answer

Is there a lid on the box or not?

anonymous · Answer

no

anonymous · Answer

ok, then the previous post about the max volume is correct. This is because the largest Volume one can get out of a limited surface area (the material you are using) is made from a cube.

anonymous · Answer

since you have 5 sides that you need to build (it would be 6 but your box has no lid), the max volume you can get is 5x^2=56.  We already know that the base is a square--and so we can say the base is x*x.

anonymous · Answer

Follow your nose from there =)

anonymous · Answer

awesome thanks :)