Figure12b
VolumeBy CylindricalShells
The methodof computingvolumesso far dependeduponcomputingthe cross-sectionalarea of the solid
and then integratingit acrossthe solid.Whathappenswhenthe cross-sectionalarea cannotbe foundor
the integrationis too difficult to solve?Hereis wheretheshellmethodcomesalong.
To showhow difficult it sometimesis to use the disk or the washermethodsto computevolumes,consider
the regionenclosedby the function Let us revolveit aboutthe line to generate
the shapeof a doughnut-shapedcake.Whatis the volumeof this solid?