University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 14 - Section 14.7 - Triple Integrals in Cylindrical and Spherical Coordinates - Exercises - Page 805: 53

Answer

$$\dfrac{\pi}{2}$$

Work Step by Step

Our aim is to integrate the integral as follows: $$ Volume=4\int^{\pi/2}_0 \int^1_0 \int^{r^2}_0 dz r \space dr d\theta \\=(4) \times \int^{\pi/2}_0 \int^1_0 r^3 \space dr \space d\theta\\=\int^{\pi/2}_0 (1) d\theta \\=\dfrac{\pi}{2}$$
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