Volume of Revolution - Maple Programming Help

Volume of Revolution

 Description Calculate the volume of revolution for a solid of revolution when a function is rotated about the horizontal or vertical axis.

Enter the function as an expression and specify the range:

 >
 ${\mathrm{sin}}{}\left({x}\right){}{\mathrm{cos}}{}\left({x}\right){+}{1}{,}{0}{..}\frac{{1}}{{2}}{}{\mathrm{π}}$ (1)

Calculate the volume of revolution:

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{VolumeOfRevolution}\right]\left(\right)$
 ${\mathrm{π}}{+}\frac{{9}}{{16}}{}{{\mathrm{π}}}^{{2}}$ (2)

Display the floating-point value using the evalf command:

 > $\mathrm{evalf}\left(\right)$
 ${8.693245131}$ (3)

Display a plot using the output=plot option:

 >

Display the exact solution (integral form) using the output = integral option:

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{VolumeOfRevolution}\right]\left(,\mathrm{output}=\mathrm{integral}\right)$
 ${{∫}}_{{0}}^{\frac{{1}}{{2}}{}{\mathrm{π}}}{\mathrm{π}}{}{\left({\mathrm{sin}}{}\left({x}\right){}{\mathrm{cos}}{}\left({x}\right){+}{1}\right)}^{{2}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{ⅆ}{x}$ (4)

Alternatively, you can use the Volume of Revolution tutor, a point and click interface.  You can launch the tutor in two ways:

 • From the Tools menu, select Tutors, Calculus - Single Variable, and then Volume of Revolution.
 • Use the following command to launch the tutor:

 > $\mathrm{Student}\left[\mathrm{Calculus1}\right]\left[\mathrm{VolumeOfRevolutionTutor}\right]\left(\right)$
 Commands Used