Study Guide for Stewart's Multivariable Calculus, 8th
Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
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Chapter 15.7, Problem 3PT
To determine

The appropriate option that completes the statement “The surface given by z=r2 in cylindrical coordinates is a(n):" from the given options (a)-(d).

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Calculate the volume of the sphere x^2 + y^2 + z^2 = a^2, using both spherical and cylindrical coordinates.
Calculate, by means of cylindrical or polar coordinates, the volume of the solid that is inferiorly bounded ´ by the plane z = 2y, and superiorly by the paraboloid z= 4+2y-x^2-y^2
Use cylindrical coordinates to show that the volume of a sphere of radius a from which a central cylinder of radius b has been removed, where 0 < b < a, only depends on the height of the band that results. In particular, this implies that such a band of radius 2 m and height 1 m has the same volume as such a band of radius 6,400 km (the radius of the earth) and height 1 m.
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