Practice question · Select all that apply
Select every statement about volumes of revolution that is true.
Hints
- Two options describe the geometry of shells and washers incorrectly.
- Recall which direction each method cuts relative to the axis.
Show the answer
- A. Disks are stacked along the axis; shells are wrapped around it.
- D. The volume element for a shell is 2 pi times radius times height times thickness.
- E. A washer is a disk with a concentric hole removed.
Why
Shells slice parallel to the axis, not perpendicular, and a washer uses rather than . The first three are exact; the fact that both methods describe the same solid is what lets you pick whichever integral is easier.
Practise Volumes of Revolution
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