How to Calculate the Volume of a Sphere with an Off-Center Hole?

In summary, the speaker was trying to calculate the volume of a sphere with an off-centered hole and was searching for information on this situation. They mentioned trying to integrate the sphere without the hole and subtracting the volume of the hole, but were determined to find an analytical solution. They asked if anyone had come across helpful information and offered to share equations if needed.
  • #1
gwiz
5
0
Recently, I was calculating the volume of a sphere with a hole through the center. I started thinking, what if the hole was off-center by some distance e. I have searched high and low and can not find anything on this situation. I have tried calculating, but after the second integral, I can not complete the third (due to complexities of the equation).

I have found the special case of Viviani's Curve, whereby e is equal to half the hole radius, and the hole radius is half the sphere radius, but that does not help.

I know this can be solved numerically (or through a CAD program), but I'm determined to try and find an analytical solution. Has anybody come across information that may help? I can post some equations if necessary.
 
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  • #2
Why not just integrate the sphere like there's no hole and then integrate just over the volume of the whole, subtracting out whatever density you put there in the first place?
 

FAQ: How to Calculate the Volume of a Sphere with an Off-Center Hole?

What is a sphere with a non-centered hole?

A sphere with a non-centered hole is a three-dimensional object that resembles a sphere, but has a cylindrical hole that is not located at the center of the sphere.

How is a sphere with a non-centered hole created?

A sphere with a non-centered hole can be created by drilling a cylindrical hole into a solid sphere at a location that is not the center of the sphere.

What are the properties of a sphere with a non-centered hole?

A sphere with a non-centered hole has the same properties as a regular sphere, such as a curved surface and constant diameter. However, it also has the added property of having a cylindrical hole that passes through its center.

What are the practical applications of a sphere with a non-centered hole?

A sphere with a non-centered hole can be used in various engineering and manufacturing applications, such as creating hollow spheres for storage or transportation, or as a component in a complex mechanism.

Are there any mathematical equations that describe a sphere with a non-centered hole?

Yes, the mathematical equation for a sphere with a non-centered hole is similar to the equation for a regular sphere, but with an added term to represent the location and size of the hole.

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