Use polar coordinates ( and double integrals ) to find the volume of the solid that is below the paraboloid z = 4 - x2 - y2 and above the xy-plane. (Hint: Note that the paraboloid intersects the xy-plane z=0 in the circle x2+y2=4; i.e., in the circle x2+y2=22. Hence, 0 <= r <= 2 and 0 <= theta <= 2pi.

Use polar coordinates ( and double integrals ) to find the volume of the solid that is below the paraboloid z = 4 - x2 - y2 and above the xy-plane. (Hint: Note that the paraboloid intersects the xy-plane z=0 in the circle x2+y2=4; i.e., in the circle x2+y2=22. Hence, 0 <= r <= 2 and 0 <= theta <= 2pi.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.1: The Rectangular Coordinate System

Problem 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...

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Question

Use polar coordinates ( and double integrals ) to find the volume of the solid that is below the paraboloid z = 4 - x² - y² and above the xy-plane.
(Hint: Note that the paraboloid intersects the xy-plane z=0 in the circle x²+y²=4; i.e., in the circle x²+y²=2². Hence, 0 <= r <= 2 and 0 <= theta <= 2pi.)

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