Solids of Known Cross Section

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Solids of Known Cross Section
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Variation on Disc Method

• With the disc method, you can find the volume of
  a solid having a circular cross section
• The same method can be generalized to solids of
  any shape as long as you know the formula for the
  area of the cross section

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Example

• Find the volume of the solid whose base is
  bounded by the graphs and
• and x 0. The cross sections
  perpendicular to the x-axis are rectangles.

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Example

• Find the volume of the solid whose base is
  bounded by the graphs and
• and x 0. The cross sections
  perpendicular to the x-axis are equilateral
  triangles.