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.
Spherical Ring

Spherical Ring Cross Section

Formulas

Spherical ring volume
Spherical ring volume
Cylinder height
Cylinder height
Cylinder volume
Cylinder volume
Sphere radius
Sphere radius 1

Sphere radius 2
Cylinder radius
Cylinder radius
Surface area
Surface area 1

Surface area 2
V = πL³/6     L = 2√(R² − r²)     S = 2πL(r + R)

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