Answer
$\frac{2\pi}{3}$
Work Step by Step
$$V=\pi\int_{0}^{1}[1-{(1-y)}^2]dy$$
$$V=\pi\int_{0}^{1}[2y-y^2]dy$$
$$V= \pi[ y^2-\frac{y^3}{3}]_{0}^{1}$$
$$V= \frac{2\pi}{3}$$.
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 7 - Applications of Integration - 7.2 Exercises - Page 454: 42
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