Answer
$$6 \pi$$
Work Step by Step
We need to integrate the integral to compute the volume.
$$Volume= (\dfrac{9\pi}{4}) \int_{0}^{2} y^2 \space dy \\ = [\dfrac{y^3}{3}]_{0}^{2} \times (\dfrac{9\pi}{4}) \\=(9\pi/4) (\dfrac{8}{3}) \\=6 \pi$$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 6 - Section 6.1 - Volumes Using Cross-Sections - Exercises - Page 356: 16
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