I am finding this one tricky.
Find the maximum volume of cube inscribed a right cone with radius 1, and height 3.
Why can't I do 3/1 = 3-x/x
If this was a cylinder, I'd have 3/1 = 3-h/r, and with a cube the sides are equal.
Oboy. It's my day for dumb mistakes today. I have no tme now but I'll show where that comes from later.
Edit: The key is to note that when the cube is fit inside a cone, the longest side
is the diagonal of its top face. Read:
http://books.google.com.au/books?id=...esult&resnum=1
http://www.math.hawaii.edu/home/putnam/1998.pdf