The Mass or Weight of the Frustum of a Pyramid calculator computes the mass or weight of a regular pyramid frustum based on the dimensions of the polygon base, the height of the frustum and the density of material.
INSTRUCTIONS: Choose units and enter the following:
Pyramid Frustum Mass or Weight (m): The calculator returns the mass 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
This Weight of the Frustum of a a Polygon based Pyramid calculator computes the weight or mass of a right pyramid frustum based on the dimensions of the frustum, a height (h) and a (mD) mean density. The base area (A) is defined by a polygon of (n) sides each of length (b).
`m = mD * n*h/12 * (b^2 + b*B + B^2) * cot(pi/n)`
|Common Mean Densities|
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
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 pop-up 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 pull-down menus.