The Pyramid Frustum Weight (Mass) formula computes the weight or mass of a right square pyramid with a frustum defined by base side length (R) and top side length (r) and height (h) in between and a mean density (mD).
INSTRUCTIONS: Choose units and enter the following:
 (r) Length of Top Sides of square top
 (R) Length of Bottom Sides of square base
 (h) Height of Pyramid Frustum
 (mD) Mean density of the substance of which the pyramid is made.
Pyramid Frustum Mass/Weight (M):The mass is calculated and returned in kilograms. However, the user can automatically convert this to any of the other mass/weight units (e.g. pounds, tons) via the pulldown menu.
The Math / Science
This formula computes the volume of the geometric shape based on the input parameters. With the computed volume, this formula then executes the simple equation below to compute the approximate mass of the object.
mass = density ⋅ volume
A Right Square Pyramid has a four sided base where all four sides are equal and have equal angled corners (90^{o}), which is a square. The pyramid is a right pyramid if the apex of the pyramid is directly above the center of the base square. The formula for the volume of a pyramid with a triangle base is:
`M = 1/3 * h*(R^2+R * r+r^2) * mD`
where:
 V = volume of square pyramid frustum
 h = height of pyramid
 r = side length of top
 R = side length of base
 mD = mean density of pyramid material
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/m^{3}
 Liquid Natural Gas  430 to 470 kg/m^{3}
MarketReady Grains
 Corn  56 lb/bu (721 kg/m^{3})
 Wheat  60 lb/bu (772 kg/m^{3})
 Barley  48 lb/bu (618 kg/m^{3})
 Oats  32 lb/bu (412 kg/m^{3})
 Rye  56 lb/bu (721 kg/m^{3})
 Soybean  60 lb/bu (772 kg/m^{3})

Metals
 Density of Aluminum  2,700 kg/m^{3}
 Density of Brass  8,530 kg/m^{3}
 Density of Bronze  8,150 kg/m^{3}
 Density of Chromium  7190 kg/m^{3}
 Density of Cobalt  8746 kg/m^{3}
 Density of Copper  8,920 kg/m^{3}
 Density of Gallium  5907 kg/m^{3}
 Density of Gold  19,300 kg/m^{3}
 Density of Iron  7,847 kg/m^{3}
 Density of Lead  11,340 kg/m^{3}
 Density of Nickle  8,908 kg/m^{3}
 Density of Palladium  12,023 kg/m^{3}
 Density of Platinum  21,450 kg/m^{3}
 Density of Steel  7,850 kg/m^{3}
 Density of Silver  10,490 kg/m^{3}
 Density of Titanium  4,500 kg/m^{3}
 Density of Tungsten  19,600 kg/m^{3 }
 Density of Uranium  19,050 kg/m^{3}
 Density of Zinc  7,135 kg/m^{3}
 Density of Zirconium  6,570 kg/m³

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/m^{3})
 grams per cubic centimeter (g/cm^{3})
 grams per liter (g/L)
 pounds per cubic feet (lb/ft^{3})
 ounces per cubic inch (oz/in^{3})
 pounds per barrel (lb/bbl)
 pounds per bushel (lb/bu)
vCalc provides for automatic conversions between density units via the pulldown menus.