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.
| Common Mean Densities |
| Metals
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| Fluids
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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.
The mean density (mD) of many common substances, elements, liquids and materials can be found by clicking HERE (e.g. the mean density of water is 1000.0 kg/m³).
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
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.