(a) Find the volume of the solid bounded below by the paraboloid z = x + y...

(a) Find the volume of the solid bounded below by the paraboloid z = x² + y² and above by the plane z = 1.

(b) Find the volume of the solid bounded below by the
elliptic paraboloid

and above by the plane z = k, where k > 0.

(c) Show that the volume of the solid in part (b) is equal to one-half the product of the area of the base times the altitude, as shown in the figure.

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