1.

If 1400 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

I'm not quite sure how to maximize volume given perimeter, but I know how to find perimeter given a volume. I'm sure its something simple that I'm over looking.

2.

A cone-shaped cup is made from a circular piece of paper of radius 20 by cutting out a sector and joining the edges

*AC*and

*BC*.

Find the maximum capacity (volume) of such a cup.

Essentially, given a radius of 20, what is the maximum volume that the cone can have. All of the other problems we've covered have involved squares or boxes. I don't even know how to start on this one.

I would really appreciate any help. Between being sick and working, I've having a hard time keeping up, especially when our book has no examples of how to do these kinds of problems.