Use cylindrical coordinates (a) Find the volume of the region E that lies between the paraboloid z 4 x 2 y 2 and the cone z 2x 2 y 2 (b) Find the centroid of E (the center of mass in the case where the density is constant)

Question: Use cylindrical coordinates. (a) Find the volume of the region E that lies between the paraboloid z = -4 - x 2 - y 2

Use cylindrical coordinates.

(a) Find the volume of the region E that lies between the paraboloid z = -4 - x² - y² and the cone z = 2√x² + y².
(b) Find the centroid of E (the center of mass in the case where the density is constant).

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