Volumes
LearningObjectives
- Learnthe basicconceptsof volumeand how to computeit with a givencross-section
- Learnhow to computevolumeby thedisk method
- Learnhow to computevolumeby thewashermethod
- Learnhow to computevolumebycylindricalshells
In this section,we will use definiteintegralsto find volumesof differentsolids.
The VolumeFormula
A circularcylindercan be generatedby translatinga circulardisk alonga line that is perpendicularto the
disk (Figure5). In otherwords,the cylindercan be generatedby movingthe cross-sectionalarea (the
disk)througha distance The resultingvolumeis calledthe volumeof solidand it is definedto be
Figure 5