The Weight or Mass of a Triangle Based Pyramid calculator computes the mass (M) of a pyramid with a triangle base that is defined by the length of the three triangle base sides (a,b,c) and height (h) from the base to the apex. The mass is computed using the volume and the mean density of the composition of the pyramid.
INSTRUCTIONS:
- (a) Length of side a
- (b) Length of side b
- (c) Length of side c
- (h) Height of pyramid
- (mD) Mean density of the composition of the pyramid. (e.g. 2,400 kg/m3 for concrete)
Mass of the Pyramid (M): The mass is returned in kilograms, and the volume in cubic meters. However, these can be automatically converted to compatible units via the pull-down menu.
The Math / Science
The formula for the mass of a triangle based pyramid is:
`m = mD * 1/3 * h * sqrt((a+b+c)/2((a+b+c)/2-a)((a+b+c)/2-b)((a+b+c)/2-c)) `
where:
- m = mass of pyramid
- h = height of pyramid
- a,b,c = sides of the triangle base
Note: this implies that the height is normal to triangle plane.
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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