Sphere and cylinder intersection

In summary, the speaker was seeking help with calculating the intersection volume of a sphere and a cylinder, and also mentioned that the solution for the intersection area of a disk and the area between two parallel lines could be useful. Another person suggested using Monte-Carlo integration, specifically referencing example 7 in chapter 15.6 of the third edition of Calculus by Robert A. Adams.
  • #1
s.py
1
0
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
 
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  • #2
You can easily calculate the volume with a Monte-Carlo integration.
 
  • #3
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.
 

1. What is the difference between a sphere and a cylinder?

A sphere is a three-dimensional shape with a curved surface and all points on the surface are equidistant from the center. A cylinder is also a three-dimensional shape, but it has two flat circular bases connected by a curved surface.

2. How do you find the intersection between a sphere and a cylinder?

To find the intersection between a sphere and a cylinder, you can use the equation for both shapes and solve for the points where the equations are equal. This will give you the coordinates of the points where the two shapes intersect.

3. Can a sphere and a cylinder intersect at more than two points?

Yes, a sphere and a cylinder can intersect at more than two points. This is possible when the two shapes are oriented in a way that allows for multiple points of intersection along their curved surfaces.

4. How do you calculate the volume of the intersection between a sphere and a cylinder?

To calculate the volume of the intersection between a sphere and a cylinder, you can use the formula for the volume of a spherical cap and subtract the volume of the cylinder. This will give you the volume of the intersection between the two shapes.

5. What real-world applications use the concept of sphere and cylinder intersection?

The concept of sphere and cylinder intersection is used in various fields such as engineering, architecture, and computer graphics. For example, in architecture, the intersection between a dome (sphere) and a cylindrical building structure can be used to create unique and visually appealing designs. In engineering, the intersection between a sphere and a cylinder can be used to calculate the volume of water in a water tank or the volume of oil in a cylindrical storage tank. In computer graphics, the concept is used to create realistic 3D models of objects that have curved and cylindrical components.

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