Chapter 12.6, Problem 46E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

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

To determine

**To find:** An surface equation obtained by rotating the line
*z*-axis.

Explanation

**Given data:**

The curve equation is

Consider the given curve equation.

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

Consider diameter of the circular cone is *k*.

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

Substitute *k* for *z* in the equation,

The radius is

So the surface equation has circular traces for

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