Help finding the diameter of a sphere based on a small section

[dibble]

I have a project where I have to reverse engineer CAD model a piece. Part of the problem is the piece I am modeling is part of another larger piece that cannot be taken apart.

I've found ways to guesstimate and come close. But, I'd really like to know if there's a formula for solving this problem accurately:

Assume a sphere of some unknown size (that's what I'm trying to calculate)

If I slice an 8mm thick cap off of the top of the sphere, I'm left with a base diameter of 40mm of that slice

.

I think that should be enough information to calculate the sphere. But, I have no idea how to tackle it. help?

 

[Dr.Peterson]

I have a project where I have to reverse engineer CAD model a piece. Part of the problem is the piece I am modeling is part of another larger piece that cannot be taken apart.

I've found ways to guesstimate and come close. But, I'd really like to know if there's a formula for solving this problem accurately:

Assume a sphere of some unknown size (that's what I'm trying to calculate)

If I slice an 8mm thick cap off of the top of the sphere, I'm left with a base diameter of 40mm of that slice

View attachment 9244.

I think that should be enough information to calculate the sphere. But, I have no idea how to tackle it. help?

You've got the height h and the diameter 2r₁ of a spherical cap, as shown here.

From this, the radius of the sphere is [FONT=&quot]r = (h[/FONT]²[FONT=&quot]+r[/FONT]₁²[FONT=&quot])/(2h)[/FONT] . You could derive this yourself by drawing in the right triangle consisting of the center of the sphere, the center of the circle, and a point on the circle, and applying the Pythagorean theorem.[FONT=&quot][/FONT]

 

[dibble]

So, I come up with 29mm radius. Never heard of a spherical cap (I'm not an engineer, I just play one on the internet)

Thanks. Doesn't look like much. But, that helped tremendously.