8. Let V be the volume of the region inside the sphere r2 + y? + z? = 6 that lies above the paraboloid z = r? + y?. (a) Write down the triple integral that corresponds to this volume, and specify the bounds of integration with the order of integration z first, y second, and r last. DO NOT evaluate this integral. (b) Find the volume of the region using cylindrical coordinates.

8. Let V be the volume of the region inside the sphere r2 + y? + z? = 6 that lies above the paraboloid z = r? + y?. (a) Write down the triple integral that corresponds to this volume, and specify the bounds of integration with the order of integration z first, y second, and r last. DO NOT evaluate this integral. (b) Find the volume of the region using cylindrical coordinates.

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 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...

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