Honors AP Calculus / Mr. Hansen 1/8/2009		Name: ______________________
	Quest (50 points)
1.	A parabolic arch, is rotated about the y-axis to create a paraboloid. A right circular cone with its vertex at the origin is to be inscribed in the paraboloid such that the cone (which is inverted) has its base in full contact around the rim with the paraboloid.
(a)	Sketch this situation.
(b)	Compute the volume of the circular cone of height 2 that meets the conditions of the problem. Use an integral formula to obtain your answer. (You may, of course, use the standard geometry formula to check your work.)
(c)	Find the height and volume of the cone of maximum volume that satisfies the conditions of the problem. Again, use an integral formula. Justify your answers.