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.
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: