Let E be a region bounded by xy-plane and a surface z= 1−x^2−y^2 a) Write the conversion formula that gives the cartesian coordinates x,y and z in terms of the cylindrical coordinates r, θ and z. b) Write E in cylindrical coordinates (what are the bounds for r ,θ and z? c) Write volume element in cylindrical coordinates d) Use parts a, b and c in order to set up an integral that would describe the volume of the region E e) Evaluate that integral

Let E be a region bounded by xy-plane and a surface z= 1−x^2−y^2 a) Write the conversion formula that gives the cartesian coordinates x,y and z in terms of the cylindrical coordinates r, θ and z. b) Write E in cylindrical coordinates (what are the bounds for r ,θ and z? c) Write volume element in cylindrical coordinates d) Use parts a, b and c in order to set up an integral that would describe the volume of the region E e) Evaluate that integral

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...

See similar textbooks