KEVOS® MAKEOS · Geometry
Volume and Surface of Solids
What volume, surface area and mass does this solid have?
Volume, surface area and mass of spheres, hollow spheres, spherical caps, zones, sectors and wedges, cones, pyramids, cylinders, cylindrical hoofs, paraboloids, barrels, tori and ellipsoids.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Solid | choice | Solid type; the option text names each dimension. |
| Dimension A | mm | First dimension as described. |
| Dimension B | mm | Second dimension where needed. |
| Dimension C | mm | Height or length where needed. |
| Wedge angle | ° | Included angle of a spherical wedge. |
| Density (for mass) | kg/m³ | Material density to give a mass (0 to skip). |
Method and formulas
- Sphere πd³/6; cap πh(3a² + h²)/6; zone πh(3a² + 3b² + h²)/6; sector 2πr²h/3; wedge (θ/360) × 4πr³/3.
- Cone and pyramid ⅓ × base × height; hoof 2r²h/3; paraboloid πr²h/2; paraboloidal segment πh(R² + r²)/2.
- Barrel with parabolic staves πL(8D² + 4Dd + 3d²) ÷ 60 (D at the bung, d at the heads); torus 2π²Rr²; ellipsoid πabc ÷ 6 with full axes.
- Example: a spherical cap of 100 mm base radius and 30 mm height holds 485.38 cm³.
Limitations
- Ideal solids; the barrel formula assumes parabolic staves.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find volumes and masses of turned and formed parts
- Estimate tank and vessel capacities
- Check CAD volumes
Who it is for
- Design engineers
- Toolmakers
- Estimators
What you get
- Volume
- Surface area (where a simple formula exists)
- Mass
Interpreting the result
- For hollow parts, subtract the inner volume or use the hollow shape options.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 82–88. Topic reference; no source tables or recommended settings are reproduced.
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