Question: Let W be the region above the sphere x 2 + y 2 + z 2 = 6 and below the paraboloid z = 4

Let W be the region above the sphere x²+ y² + z²= 6 and below the paraboloid z = 4 − x²− y².
(a) Show that the projection of W on the xy-plane is the disk x²+ y²≤ 2 (Figure 19).
(b) Compute the volume of W using polar coordinates.

2 W z=4-x-y x + y +2=6 6

2 W z=4-x-y x + y+z = 6 6

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