Sphere and cylinder intersection

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SUMMARY

The intersection volume of a sphere and a cylinder can be effectively calculated using Monte-Carlo integration techniques. A specific reference for this method is found in example 7 of chapter 15.6 in the third edition of "Calculus" by Robert A. Adams. This approach simplifies the problem significantly, providing a practical solution for those struggling with the calculations. Additionally, understanding the intersection area of a disk and the area defined by two parallel lines can also aid in grasping the concept.

PREREQUISITES
  • Monte-Carlo integration techniques
  • Basic calculus principles
  • Understanding of geometric shapes (sphere and cylinder)
  • Familiarity with "Calculus" by Robert A. Adams
NEXT STEPS
  • Study Monte-Carlo integration methods in depth
  • Review example 7 in chapter 15.6 of "Calculus" by Robert A. Adams
  • Explore geometric intersection problems in calculus
  • Learn about the intersection area of disks and parallel lines
USEFUL FOR

Mathematicians, engineering students, and anyone interested in advanced calculus and geometric problem-solving will benefit from this discussion.

s.py
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Hi,

Recently i tried (and failed) to calculate the intersection volume of a sphere and a cylinder.

I found this simple problem seems not so simple for me. Searching on the web, nothing on that, so if someone can help me thank you.

(the simplified solution with the intersection area of a disk and the area delimited by two paralleles could help me too)

s.pierre-yves
 
Physics news on Phys.org
You can easily calculate the volume with a Monte-Carlo integration.
 
Have a look at example 7 chapter 15.6 in the third edition of Calculus by Robert A. Adams (should be in newer editions as well, but then the example number and chapter number could be different), it's exactly this kind of problem.
 

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