Practice question · Put in order
Order the steps for computing a volume of revolution.
- Choose disks or shells according to how the slices meet the axis
- Integrate the volume element between the limits of the region
- Sketch the region and identify the axis of rotation
- Write the radius (and height, for a shell) as a function of the variable
- Assemble the volume element for one slice
Hints
- The axis has to be known before a method can be chosen.
- A single slice is described in full before any integration happens.
Show the answer
- Sketch the region and identify the axis of rotation
- Choose disks or shells according to how the slices meet the axis
- Write the radius (and height, for a shell) as a function of the variable
- Assemble the volume element for one slice
- Integrate the volume element between the limits of the region
Why
The pattern is the same as Riemann sums: slice, express one slice's volume, integrate. Every setup error in this lesson happens in the middle steps, misidentifying the radius or attaching the wrong volume element to the slice.
Practise Volumes of Revolution
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