Volume Integral

  • #1
Use an appropriate volume integral to find an expression for the volume enclosed between a sphere of radius 1 centered on the origin and a circular cone of half-angle alpha with its vertex at the origin. Show that in the limits where alpha = 0 and alpha = pi that your expression gives the expected values.

Any ideas or clues? Where alpha = pi I think the volume will be half the volume of the sphere.
 

Answers and Replies

  • #3
that's actually very helpful, thanks
 
  • #4
34,965
6,720
Use an appropriate volume integral to find an expression for the volume enclosed between a sphere of radius 1 centered on the origin and a circular cone of half-angle alpha with its vertex at the origin. Show that in the limits where alpha = 0 and alpha = pi that your expression gives the expected values.

Any ideas or clues? Where alpha = pi I think the volume will be half the volume of the sphere.
Please post homework or homework-like problems in the Homework & Coursework sections, not here in the technical math sections.
 

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