   Chapter 16.6, Problem 24E

Chapter
Section
Textbook Problem

Find a parametric representation for the surface.24. The part of the cylinder x2 + z2 = 9 that lies above the xy-plane and between the planes y = −4 and y = 4

To determine

To find: The parametric representation for part of the cylinder x2+z2=9 that lies above the xy-plane and between the planes y=4 and y=4 .

Explanation

Given data:

The part of the cylinder x2+z2=9 that lies above the xy-plane and between the planes y=4 and y=4 .

For the given data, consider y as parameters and parameterize the part of the cylinder x2+z2=9 as follows.

Consider t as a scalar parameter and choose the parameters for x and y such that the parameters should satisfy the equation of cylinder x2+z2=9 . Therefore, the parameters are considered as follows.

x=3costy=yz=3sint

The parameters are satisfied the cylinder equation x2+z2=9 for the limit of scalar parameter 0tπ

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