Mathematics I / Volumes of Revolution
Practice question · Select all that apply

Select every statement about volumes of revolution that is true.

Hints
  1. Two options describe the geometry of shells and washers incorrectly.
  2. 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 R2r2R^{2} - r^{2} rather than (Rr)2(R-r)^{2}. The first three are exact; the fact that both methods describe the same solid is what lets you pick whichever integral is easier.

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