`M = f( "a" , "b" , "h" , "t" , 7850 )`

Enter a value for all fields

The Weight of a Cone Shell calculator computes the mass (weight) of the shell of a right circular cone or cone frustum defined by a top radius (a) and base radius (b), height (h) in between, the thickness (t) and the mean density (mD). NOTE: NEW DEFAULT UNITS.

INSTRUCTIONS: Choose units and enter the following:

• (a) Top outer radius
• (b) Bottom outer radius
• (h) Height of the cone or cone section
• (t) Thickness of the shell
• (mD) The mean density of the substance of the cone (CLICK HERE).

Cone Shell Weight (M):The calculator computes the mass/weight of the cone in kilograms.  However, this can be automatically converted to numerous other mass/weight units (e.g. pound, tons) via the pull-down menu.  Note: For a complete cone, simply let the top radius (a) remain as zero.

The Math

Note: the frustum is created by parallel planes that go through the cone and are normal (perpendicular) to the center axis of the cone.  The planes are separated by the height (h). The formula for the Volume of the Frustum of a cone is as follows:
          V = ¹/₃ • π • h(a²+a•b+b²)

The Mass of a Cone Shell calculator:

1. Computes the Volume of the shell

• • Computes the Volume of the Outer Shell
  • Subtracts the Volume of the Inner Shell

1. Uses the volume times the density to compute the mass or weight of the shell

NEW DEFAULT UNITS

As of 16 July 2024, the default input units have been changed from meters (m) to millimeters (mm) and the default density of material has been set to 7850 kg/m³, which is the density of steel.  This change was made to accommodate the most frequent users of this calculator.

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Mean Density Table

Common Mean Densities in Kilograms per Meter Cubed (kg/m3)
Fluids Pure Water - 1,000   Seawater - 1,022   Milk - 1,037  Olive Oil - 860 Cement Slurry - 1,442  Fuels Diesel Fuel - 885  Crude Oil - 870 to 920   Fuel Oil -  890   Ethanol - 789   Gasoline (petrol) - 737  Propane - 493  Liquid Natural Gas - 430 to 470  Market-Ready Grains Corn - 721 (56 lb/bu) Wheat - 772 (60 lb/bu) Barley - 618 (48 lb/bu) Oats - 412 (32 lb/bu) Rye - 721 (56 lb/bu) Soybean - 772 (60 lb/bu)	Metals Density of Aluminum - 2,700 Density of Brass - 8,530  Density of Bronze - 8,150  Density of Chromium - 7,190  Density of Cobalt - 8,746  Density of Copper - 8,940   Density of Gallium - 5907  Density of Gold - 19,300 Density of Iron - 7,847 Density of Lead - 11,340 Density of Nickle - 8,908  Density of Palladium -  12,023 Density of Platinum - 21,450  Density of Steel - 7,850  Density of Silver - 10,490  Density of Tin - 7,280 Density of Titanium - 4,500  Density of Tungsten - 19,600  Density of Uranium - 19,050 Density of Zinc - 7,135  Density of Zirconium - 6,570	Earthen Concrete - 2,371 Dirt - 1,250 Fire Clay - 1,362 Glass - 2,500 Granite - 2,691 Sand (dry) - 1,602 Sand (wet) - 2,082 Sandstone - 2,323 Synthetic Bakelite - 1,362 Carbon Fiber - 2,000 Organic Balsa - 170 Cork - 240 Mahogany - 545 Oak - 760 Pine - 539 Rubber - 1,522
Mean Density Lookup Function

Mean density is scientifically volume divided by mass.  There are  various unit for density adopted by cultures and industries. Common units for density included the following:

• kilograms per cubic meter (kg/m³)
• grams per cubic centimeter (g/cm³)
• grams per liter (g/L)
• pounds per cubic feet (lb/ft³)
• ounces per cubic inch (oz/in³)
• pounds per barrel (lb/bbl)
• pounds per bushel (lb/bu)

If you want to identify a material by its density, use the Density Within Range tool.

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Cone Calculators

1. Cone Surface Area based on cone height and cone base radius
2. Cone Volume based on cone height and cone base radius
3. Cone Mass or Weight as a function of the volume and mean density
4. Cone Frustum Surface Area based on the two heights and two radii
5. Cone Frustum Volume based on the two heights and two radii 
6. Cone Frustum Weight or Mass based on the cone frustum volume and mean density
7. Cone Shell Volume a.k.a. hollow cone volume
8. Cone Shell Mass or Weight a.k.a. hollow cone mass
9. Moment of inertia of a cone shaped object based on mass and rotation axis
10. Moment of inertia of a cone shaped object based on mass and distance to apex (rotation around apex)
11. Compute the total surface are of the frustum of a cone:  This includes the top and bottom surfaces.
12. Compute the lateral surface area (using L) of the frustum of a cone.

See Also

• Frustum Calculator - Equations for volume, mass and surface areas for various frustums.
• Volume Calculator - Volume equations for various geometric shapes
• Mass Weight Calculator - Equations for the mass and weight of objects based on their mean density and shape

Reference

• Equation 4.42 Spiegel, Murray R. "Chapter 4." Mathematical Handbook of Formulas and Tables. New York: McGraw-Hill, 1968. N. pag. Print.