Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 15 - Multiple Integrals - 15.8 Exercises - Page 1055: 13

Answer

Cylindrical coordinates: $6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,0 \leq z \leq 20$}

Work Step by Step

Let us consider the $z-axis$ to be the axis of the cylindrical shell along with the center at the origin. Conversion of rectangular to cylindrical coordinate system gives $r^2=x^2+y^2 \\ \tan \theta=\dfrac{y}{x} \\z=z$ Thus, we have the cylindrical coordinates inside the shell: {$(r, \theta, z) \in E|6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,-10 \leq z \leq 10$} Hence, the Cylindrical coordinates are: $6 \leq r \leq 7, 0 \leq \theta \leq 2\pi,0 \leq z \leq 20$}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.