Answer
$$4 \pi.$$
Work Step by Step
The surface will be a disk with raduis $r=2 $, so the area $A$ is $$A=\pi r^2=2^2 \pi=4 \pi.$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.2 Arc Length and Speed - Preliminary Questions - Page 610: 6
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