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 pull-down 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.
A Right Square Pyramid has a four sided base where all four sides are equal and have equal angled corners (90o), 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
| Common Mean Densities | |
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Fluids
Fuels
Market-Ready Grains |
Metals
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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:
- μD = mean density
- V = Volume in units like cubic meters or cubic inches
- m = Mass in units like kilograms or pounds
Mean density is also often indicated as the Greek symbol rho (ρ).
Mass and Weight
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 Units
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.
Pyramid Calculators
- Volume of a Pyramid
- Mass or Weight of a Pyramid
- Volume of a Frustum of a Pyramid
- Mass of a Frustum of a Pyramid
- Volume of a Polygon Based Pyramid
- Mass of a Polygon Based Pyramid
- Volume of a Frustum of a Polygon Based Pyramid
- Mass of a Frustum of a Polygon Based Pyramid
- Mean Density of Many Substances: The Mean Density Lookup equation provides the mean density of hundreds (650+) substances from metals to gases, woods, food, liquids and much more. The results of the Mean Density look-up are in kg/m3. Use the answer for the substance you choose in the mass equation to approximate the mass or weight of the pyramid shaped object based on its shape, dimensions and the mean density of its composition.