   Chapter 11.6, Problem 32E

Chapter
Section
Textbook Problem

# Finding an Equation for a Surface of Revolution In Exercises 31–36, find an equation for the surface of revolution formed by revolving the curve in the indicated coordinate plane about the given axis. Equation of Curve Coordinate Plane Axis of Revolution 32. z 2 = 9 y yz-plane y-axis

To determine

To calculate: The equation for the surface of revolution formed by revolving the curve z=3y in the yz-plane about the y-axis.

Explanation

Given:

The equation of the curve z=3y in the coordinate plane yz about the y-axis.

Formula used:

Surface revolution forms are shown below:

Calculation:

Consider the equation of the curve z=3y,

Substitute y=0,

z=3y=3(0)=0

Similarly, substitute y=1,

z=3y=3(1)=3

Similarly, substitute y=2,

z=3y=3(2)

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