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 Table
Common Mean Densities in Kilograms per Meter Cubed (kg/m^{3}) 
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
MarketReady Grains

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/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)
If you want to identify a material by its density, use the Density Within Range tool.
A regular pyramid is a type of pyramid that has the following characteristics:
 Base: The base of a regular pyramid is a regular polygon, meaning all sides of the polygon are equal in length, and all interior angles are equal. Examples of regular polygons include equilateral triangles, squares, and regular pentagons.
 Apex: The apex is the point directly above the center of the base. In a regular pyramid, the apex is aligned such that the line segment (height) from the apex to the center of the base is perpendicular to the base.
 Lateral Faces: The lateral faces of the pyramid are congruent isosceles triangles. Each triangle shares a side with the base of the pyramid and meets at the apex.
 Height: The height of the pyramid is the perpendicular distance from the apex to the center of the base.
Because of these properties, a regular pyramid is symmetric around its vertical axis (the line connecting the apex to the center of the base).