Distance Between Parallel Planes Intersecting A Sphere

[SaxonViolence]

Friends,

 

Imagine a sphere with a radius of R. A circle that results from the intersection of a plane, that passes through the sphere's origin, with the sphere will be a circle with radius R. Now imagine that a second plane is parallel to the first plane, and the circle formed by the intersection of the second plane and the sphere is a circle with radius R'. Given the two radiuses can I find the distance between my two planes?

 

I'm not sure that's clear, so let me put it in context. Say that I wanted build a building in the shape of a hemisphere. Radius on the ground floor is 15'. Lets say that I want the second floor to have a radius of 10'. How far apart would I need to put my floors to accomplish that?

 

With a formula I would know if the floors were too close together or wastefully far apart—leaving room for a full floor between.

 

Thanks.

 

Saxon Violence

[Vmedvil]

Ya, you cannot know the distance between the two from the radius of circles at parallel but if it were a constant slope it would be 5' making a circular cone from 10' to 15' and this shape if it were a continuous slope. 

 

 

The equation for this shape containing both circles would be.

 

 

which R - R' = r

 

and  H - H' = h

 

Edited October 22, 2017 by Vmedvil

[Maine farmer]

Ya, you cannot know the distance between the two from the radius of circles at parallel but if it were a constant slope it would be 5' making a circular cone from 10' to 15' and this shape if it were a continuous slope. 

 

 

I'm not sure because my calculus is so rusty, but isn't there a way to use integration to formulate a solution to the problem?  There must be, but I'm just way to tired right now to dust off that part of my brain.  If you consider the sphere to be made up of a whole bunch of parallel  circles... ?

 

Well... I slept on it, and didn't need calculus at all.  

 

If you square the radius of your intended floor, it should equal the square of the central radius squared minus the square of the distance between the floors.

Edited October 23, 2017 by Farming guy

[SaxonViolence]

Thank you.