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:
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.
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.
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:
Common Mean Densities  
Fluids
Fuels
MarketReady Grains 
Metals

Mean Density is the average amount of mass within a volume for a substance. Note, volume of a material is often highly subject to the temperatures, since materials expand as they warm. For that reason, mean densities of substances are often cited with a set of nominal conditions such as temperature and barometric pressure.
The formula for mean density is:
μD = V / m
where:
Mean density is also often indicated as the Greek symbol rho (ρ).
Density is a function of mass. However, converting from mass to weight is trivial under the right conditions. Fortunately those conditions are generally true anywhere on the surface of the Earth, so the conversions built into the vCalc engine can be assumed to be fairly accurate unless you require weight at very high altitudes or in space.
CLICK HERE for a popup function that provides the mean density (mD or μD) of many common substances, elements, liquids and materials.
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:
vCalc provides for automatic conversions between density units via the pulldown menus.