Answer
$$z=\frac{1}{2}\ln({x^2+y^2})$$
Work Step by Step
By the definition of revolution about z-axis,
$$y\rightarrow \sqrt{y^2+x^2}$$
Substituting in $z=\ln{y}$, we get
$$z=\frac{1}{2}\ln({x^2+y^2})$$
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 11 - Vectors and the Geometry of Space - 11.6 Exercises - Page 803: 36
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