Please only answer part 3 and 4 but in details. I will upvote you thanks.

In this project, you play the role of a consultant to a bedding manufacturer. The manufacturer is interested in constructing a sleeping pod. You will use a number of tools from Calculus III (including optimization and parameterization) to advise the client on the construction of such a pod. The pod is to have an outer shell in the shape of the ellipsoid xz + y2 + zz = 3. 1. Use a graphing utility to graph the ellipsoid in 3-space. 2. Derive a parameterization of the ellipsoid in terms of (p and 9 (in spherical coordinates). 3. Find the volume of the ellipsoid. You need to exhibit the appropriate integration to nd this volume. 4. The pod is to have walls that are uniformly 0.15 units thick. The construction material for the walls costs $1.17 per cubic unit. What is the cost to produce the walls of the pod? 5. Find the point(s) on the inner shell of the pod that is farthest from the origin and such that 0