I need to find the volume of an egg with a shape described by:
z = 1/2(x2 + y2) and z = 6 - x2 - y2
I am also given that the egg is 6cm in length.
I roughly graphed the two surfaces. The first being paraboloid that opens up from the origin, and the second being a paraboloid that opens down from z =6. The region under these two surfaces is the "egg."
The Attempt at a Solution
I don't know where to begin to set this up. I know that the region I need is the region in between the two curves. I assume I integrate dz from 0 to 6. I don't know where to go from there.