Spherical Ring
Properties and formulas for calculating a spherical ring (napkin ring)
Definition and Properties
A spherical ring is a solid sphere with a cylindrical hole drilled through its center. It is bounded by the outer spherical surface and the inner cylindrical lateral surface.
Important variables:
- R = sphere radius
- r = cylinder radius
- L = ring height (hole height)
Special fact:
The ring volume depends only on height L, not on radius R.
This is why spherical rings with the same height always have the same volume.
Formulas
Spherical ring volume
Cylinder height
Cylinder volume
Sphere radius
Cylinder radius
Surface area
V = πL³/6 L = 2√(R² − r²) S = 2πL(r + R)
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