Calc_Lecture_07 - Surfaces of Revolution 1 Surfaces of...

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1 Surfaces of Revolution
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2 Surfaces of Revolution The fifth special type of surface you will study is called a surface of revolution. You will now look at a procedure for finding its equation. Consider the graph of the radius function y = r ( z ) Generating curve in the yz -plane.
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3 Surfaces of Revolution If this graph is revolved about the z -axis, it forms a surface of revolution, as shown in Figure 11.62. The trace of the surface in the plane z = z 0 is a circle whose radius is r ( z 0 ) and whose equation is x 2 + y 2 = [ r ( z 0 )] 2 . Circular trace in plane: z = z 0 Replacing z 0 with z produces an equation that is valid for all values of z. Figure 11.62
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4 Surfaces of Revolution In a similar manner, you can obtain equations for surfaces of revolution for the other two axes, and the results are summarized as follows.
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5 a. An equation for the surface of revolution formed by revolving the graph of about the z -axis is Example 5 – Finding an Equation for a Surface of Revolution
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Example 5 – Finding an Equation for a Surface of Revolution b. To find an equation for the surface formed by revolving the graph of 9 x 2 = y 3 about the y -axis, solve for x in terms of y to obtain So, the equation for this surface is The graph is shown in Figure 11.63. Figure 11.63
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This note was uploaded on 10/05/2011 for the course BIO 203, CH taught by Professor Lacey,simmerling,deng,hanson during the Fall '10 term at SUNY Stony Brook.

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Calc_Lecture_07 - Surfaces of Revolution 1 Surfaces of...

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