University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 6 - Section 6.1 - Volumes Using Cross-Sections - Exercises - Page 355: 9


$$8 \pi $$

Work Step by Step

We need to integrate the integral to compute the volume. $$Volume = \int_{0}^{2} (\dfrac{5\pi y^4}{4}) \times y^4 dy \\= (\dfrac{5\pi}{4}) \times [(\dfrac{y^5}{5}]_{0}^{2} \\= \pi \times \dfrac{5}{4} \times (\dfrac{32}{5}) \\=8 \pi $$
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