Volume of a Solid of Revolution
Rotation about x=0
� 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 axis is rotated about the axis. 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

Result

Form the definite integral representing the volume, and evaluate.
Use the Expression palette to construct the definite integral. Press [Enter] to evaluate.


(3.1.1) 

Solution (b)
Using shells, the volume is given by
where and
Step

Result

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. In plot options, select "Boxed" for axes and select "Use constrained scaling". Press [Display]. See Figure 1 below.



For corroboration, form the definite integral representing the volume, and evaluate.
Use the Expression palette to construct the definite integral. Press [Enter] to evaluate.


(3.2.1) 

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