Examples for

Surfaces & Solids of Revolution

Surfaces of revolution and solids of revolution are some of the primary applications of integration. A two-dimensional curve can be rotated about an axis to form a solid, surface or shell. Use Wolfram|Alpha to accurately compute the volume or area of these solids. Examples of the methods used are the disk, washer and cylinder method.

Surfaces of Revolution

Find the surface area of a plane curve rotated about an axis.

Compute properties of a surface of revolution:

rotate y=2x, 0<x<3 about the y-axis
revolve f(x)=sqrt(4-x^2), x = -1 to 1, around the x-axis

Solids of Revolution

Calculate the volume enclosed by a curve rotated around an axis of revolution.

Compute properties of a solid of revolution:

rotate the region between 0 and sin x with 0<x<pi around the x-axis
revolve region between y=x^2 and y=x, 0<x<1, about the y-axis

RELATED EXAMPLES

  • Area between Curves
  • Curves & Surfaces
  • Integrals
  • Limits
  • Solid Geometry