Chapter 13.6, Problem 67E

Designing a snow cone A surface, having the shape of an oblong snow cone, consists of a truncated cone, $\frac{x^2}{2}+y^2=\frac{z^2}{8}$for 0 ≤ z ≤ 3, capped off by the upper half of an ellipsoid. Find an equation for the upper half of the ellipsoid so that the bottom edge of the truncated ellipsoid and the top edge of the cone coincide, and the distance from the top of the cone to the top of the ellipsoid is 3/2.