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How to build a solid ... Revolving Cube
12

AP Calculus Slides February 6, 2008

May 18, 2015

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Introduction to solids of revolution.
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Page 1: AP Calculus Slides February 6, 2008

How to build a solid ...

Revolving Cube

Page 2: AP Calculus Slides February 6, 2008

Find the area between the curves ...

Page 3: AP Calculus Slides February 6, 2008

Find the area between the curves ...

Page 4: AP Calculus Slides February 6, 2008
Page 5: AP Calculus Slides February 6, 2008

Find the area between the curves ...

Page 6: AP Calculus Slides February 6, 2008

Find the area between the curves ...

Page 7: AP Calculus Slides February 6, 2008
Page 8: AP Calculus Slides February 6, 2008

Volume of a Cone

Page 9: AP Calculus Slides February 6, 2008
Page 10: AP Calculus Slides February 6, 2008
Page 11: AP Calculus Slides February 6, 2008

Any function rotated about the x-axis will have circular cross sections and it's volume can be found by:

In General:

A(x) is the function representing the changing areas

... so you need a function that represents r.

With circular cross sections

Page 12: AP Calculus Slides February 6, 2008