Spherical Zone Volume Calculator

Find the volume and lateral surface area of a spherical zone, the middle slice of a sphere cut by two parallel planes, from its two base radii and height.

Input

Enter the bottom radius a, top radius b and height h to compute the volume and lateral surface area of a spherical zone, the middle part of a sphere cut by two parallel planes.

Bottom radius a

Top radius b

Height h

Result

Volume V

82.728607

Lateral surface area S

60.998696

Sphere radius R

4.854122

Lengths use the same unit as the inputs; areas are in squared units and the volume is in cubed units.

How it works

A spherical zone is the middle part of a sphere cut by two parallel planes. Let a be the bottom radius, b the top radius and h the distance between the planes (the height).
The volume is V equals pi h over 6 times 3a squared plus 3b squared plus h squared.
The lateral surface area, meaning the curved spherical band only, is S equals 2 pi R h, where R is the radius of the original sphere.
The original sphere radius R is found from the distances of each plane to the center using a squared equals R squared minus da squared, b squared equals R squared minus db squared and h equals da minus db.
Lengths use the same unit as the inputs, areas are in squared units and the volume is in cubed units.

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