Volume of a Solid of Revolution
Rotation about x=2
? Maplesoft, a division of Waterloo Maple Inc., 2007
Introduction
This application is one of a collection of examples teaching Calculus with Maple. These applications use Clickable Calculus? methods to solve problems interactively. Steps are given at every stage of the solution, and many are illustrated using short video clips. Click on the
buttons to watch the videos.
Problem Statement
A solid of revolution is formed when the region bounded by the curves 
and the x-axis is rotated about the line 
. Using the method of (a) disks, and (b) shells, find 
, its volume.
Solution
Solution (a)
The volume of revolution is given by
where 
and 
Step
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Result
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Form the integral and evaluate.
Use the definite integral template from the Expression palette to define the integral. Remember to change the variable of integration to  Press [Enter] to evaluate the integral.
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(3.1.1) |
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Solution (b)
Using shells, the volume is given by
where 
and 
.
Step
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Result
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Launch and use the Volume of Revolution Tutor.
Tools>Tutors> Calculus- Single Variable>Volume of Revolution. Enter  and  Set a=0 and b=1. Select "Vertical" for Line of Revolution and set Distance of rotation line fro coordinate axis to 2. In plot options, select "Boxed" for axes and "Used constrained scaling." Press [Display]. See Figure 1 below.
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Figure 1 Volume of Revolution Tutor used to compute the volume of the solid of revolution formed when the region bounded by the curves  and the x-axis is rotated about the line  .
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For corroboration, form the integral and evaluate.
Use the definite integral template in the Expression palette to define the integral. Press [Enter] to evaluate.
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(3.2.1) |
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