   Chapter 12.6, Problem 46E

Chapter
Section
Textbook Problem

# Find an equation for the surface obtained by rotating the line z = 2y about the z-axis.

To determine

To find: An surface equation obtained by rotating the line z=2y about the z-axis.

Explanation

Given data:

The curve equation is z=2y .

Consider the given curve equation.

z=2y (1)

The 2D plot for equation (1) is drawn as shown in Figure 1.

This line plot (Figure 1) produces a circular cone with vertex at origin while rotating about the z-axis.

The sketch the surface obtained the line z=2y is drawn as shown in Figure 1.

Consider diameter of the circular cone is k.

Rearrange equation (1) to find radius of the circular cone.

2y=zy=z2

Substitute k for z in the equation,

y=k2

So the surface equation has circular traces for z=k

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