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THE FEUTEX TOOLKIT

Spherical Zone Surface and Volume

Find the sphere surface band and solid volume between two parallel cut planes.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
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FormulaSurface = 2*PI*r*(z2-z1); Volume = PI*(r**2*(z2-z1)-(z2**3-z1**3)/3)
Sources and model references

Made for real tasks

  • Find the sphere surface band and solid volume between two parallel cut planes.
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Worked example

Inputs

Sphere radius
5 length
Lower height from center
-1 length
Upper height from center
2 length

Expected results

Surface
94.24777961 length²
Volume
226.1946711 length³

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter sphere radius, lower height from center, upper height from center.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "r": 5,
  "z1": -1,
  "z2": 2
}

Accuracy and scope

Uses finite-precision arithmetic. Results describe the stated mathematical model, not measurement accuracy.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.