The Mass or Weight of an Ellipsoid Cap calculator computes the mass or weight of an ellipsoid cap where the semi-axes of the ellipsoid are a, b, and c, and the height of the cap is h. The mean density is also used.
INSTRUCTIONS: Choose units and enter the following:
- (a) semi-axis a.
- (b) semi-axis b.
- (c) semi-axis c.
- (h) height of the cap
- (mD) mean density of the cap material [CLICK HERE ]
Mass or Weight of an Ellipsoid Cap (M): The mass is returned in kilograms. However, the volume can be automatically converted to compatible units via the pull-down menu.
The Math / Science
his calculator first computes the volume of an ellipsoid cap based on the following formula:
`V = π⋅a⋅b⋅((2c)/3-x+(x³)/(3c²))`
where:
With the volume of the ellipsoid cap, this formula then executes the simple equation below to compute the approximate mass of the object.
Mass = Volume ⋅ Density
To query the mean density (mD or μD) of many common substances, elements, liquids and materials, CLICK HERE (e.g. the density of water is 1,000 kg/m³.
When the formula for mass and volume of a Ellipsoid Cap are combined, one has formula for the mass of an ellipsoid cap is:
M = `π⋅a⋅b⋅((2c)/3-x+(x³)/(3c²))⋅mD`
where:
Mean Density Units
Common Mean Densities |
Fluids
- Pure Water - 1,000 kg/m³
- Seawater - 1,022 kg/m³
- Milk - 1,037 kg/m³
- Olive Oil - 860 kg/m³
- Cement Slurry - 1,442 kg/m³
Fuels
- Diesel Fuel - 885 kg/m³
- Crude Oil - 870 kg/m³ to 920 kg/m³
- Fuel Oil - 890 kg/m³
- Ethanol - 789 kg/m³
- Gasoline (petrol) - 737 kg/m³
- Propane - 493 kg/m3
- Liquid Natural Gas - 430 to 470 kg/m3
Market-Ready Grains
- Corn - 56 lb/bu (721 kg/m3)
- Wheat - 60 lb/bu (772 kg/m3)
- Barley - 48 lb/bu (618 kg/m3)
- Oats - 32 lb/bu (412 kg/m3)
- Rye - 56 lb/bu (721 kg/m3)
- Soybean - 60 lb/bu (772 kg/m3)
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Metals
- Density of Aluminum - 2,700 kg/m3
- Density of Brass - 8,530 kg/m3
- Density of Bronze - 8,150 kg/m3
- Density of Chromium - 7190 kg/m3
- Density of Cobalt - 8746 kg/m3
- Density of Copper - 8,920 kg/m3
- Density of Gallium - 5907 kg/m3
- Density of Gold - 19,300 kg/m3
- Density of Iron - 7,847 kg/m3
- Density of Lead - 11,340 kg/m3
- Density of Nickle - 8,908 kg/m3
- Density of Palladium - 12,023 kg/m3
- Density of Platinum - 21,450 kg/m3
- Density of Steel - 7,850 kg/m3
- Density of Silver - 10,490 kg/m3
- Density of Titanium - 4,500 kg/m3
- Density of Tungsten - 19,600 kg/m3
- Density of Uranium - 19,050 kg/m3
- Density of Zinc - 7,135 kg/m3
- Density of Zirconium - 6,570 kg/m³
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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)
vCalc provides for automatic conversions between density units via the pull-down menus.
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