   Chapter 11.6, Problem 34E

Chapter
Section
Textbook Problem

# Finding an Equation of a Surface of Revolution In Exercises 31-36, find an equation for the surface of revolution formed by revolving the curve in the indicated coordinated plane about the given axis. Equation Coordinate Axis of of Curve Plane Revolution 2 z = 4 − x 2                           x z − p l a n e                                             x − a x i s

To determine

To calculate: The equation of the surface of revolution formed by revolution of the curve 2z=4x2 around the x-axis and coordinate plane is xz-plane.

Explanation

Given:

The curve to be revolved is 2z=4x2 and its axis of revolution is x-axis and coordinate plane is xz-plane.

Formula used:

The equation of the resulting surface of revolution has one of the forms listed below.

When revolved about the x-axis, it is y2+z2=[r(x)]2

When revolved about the y-axis, it is x2+z2=[r(y)]2

When revolved about the z-axis, it is x2+y2=[r(z)]2

Calculation:

Consider the provided equation 2z=4x2.

Now, to obtain an equation for the surface of revolution formed by revolving the graph of 2z=4x2, solve for z in terms of x to obtain z=4x22.

Now, to obtain an equation of the surface of revolution formed by revolution of the curve 2z=4x2 about the x-axis, the form used is y2+z2=[r(x)]2

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