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 357: 59


$$\dfrac{2 \pi \space R^3}{3}$$

Work Step by Step

We know that the area of the cross-section of the hemisphere is given as follows: $$Area=R^2\pi- h^2 \pi=\pi (R^2-h^2)$$ Now, we will integrate the integral to calculate the volume as follows: $$Volume = V_{\space cylinder}-V_{\space Cone} \\=\pi R^2- \dfrac{ \pi R^2}{3} (R) \\=\dfrac{2 \pi \space R^3}{3}$$
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