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Cone and Circular Frustum Volume in Separate Sections

Cone and Circular Frustum Volume in Separate Sections. Convert compatible units, recover unknown dimensions and distinguish curved surfaces, bases and total measures.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Example in initial displayed units: Radius (r) 3, Cone perpendicular height 4, Base radius (R) 3, Top radius (r) 1, Frustum perpendicular height 4 gives Cone volume 37.699112, Frustum volume 54.454273.

Vcone = πr²h/3; Vfrustum = πh(R²+Rr+r²)/3

Worked example

Enter these known values and leave the other values blank.

Radius (r)
3 cm
Cone perpendicular height
4 cm
Base radius (R)
3 cm
Top radius (r)
1 cm
Frustum perpendicular height
4 cm
Cone volume
37.7 cm³
Frustum volume
54.45 cm³

Assumptions and limitations

  • The cone and frustum sections calculate independently. Heights are perpendicular to the base planes. Frustum end radii are interchangeable in the volume formula; both are positive and equal radii produce a cylinder.
  • Select units before entering dimensions. Clear an unknown result before solving backward, and supply enough independent measurements. Display rounding does not represent measurement uncertainty.
  • Calculations use 64 significant digits and full-precision π. Original reference drawings explain dimensions and are not drawn to the entered scale.

Common questions

Can I enter cone and frustum dimensions together?

Yes. The two sections maintain separate heights and results. Frustum height and both radii are required, while a cone needs radius and height.

References

The US fluid ounce uses one 128th of the exact US liquid gallon, replacing the rounded captured reciprocal factor. The US customary cup uses one sixteenth of the exact US liquid gallon, replacing the rounded captured cup volume. Bookify replaces the captured rounded US gallon with the exact 3.785411784-liter definition.

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