Question: A solid E lies within the cylinder x 2 + y 2 = 1, below the plane z = 4, and above the paraboloid z

A solid E lies within the cylinder x² + y² = 1, below the plane z = 4, and above the paraboloid z = 1 – x² – y². (See Figure 8.) The density at any point is proportional to its distance from the axis of the cylinder. Find the mass of E.

Figure 8

z = 4 XX N (0,0,4) I T T T (0, 0, 1) (1,0,0) -z=1-p y

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