Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 15: Multiple Integrals - Section 15.7 - Triple Integrals in Cylindrical and Spherical Coordinates - Exercises 15.7 - Page 921: 50

Answer

$\frac{a^3\pi}{18}$

Work Step by Step

$ V=\int^{\pi/6}_0 \int^{\pi/2}_0 \int^a_0 p^2 \sin\phi $ $ dp $ $ d\phi d\theta $ =$\frac{a^3}{3}\int^{\pi/6}_0 \int^{\pi/2}_0 \sin\phi d\phi d\theta $ =$\frac{a^3}{3}\int^{\pi/6}_0 d\theta $ =$\frac{a^3\pi}{18}$
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.