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Polygon Pyramid Frustum Weight

vCalc Reviewed
`m = 7850 * "n" * "h" /12 * ( "b" ^2 + "b" * "B" + "B" ^2) * cot(pi/ "n" )`
`(n) "number of sides"`
`(b) "side"`
`(B) "side"`
`(h) "height"`
`(mD)"mean density"`

The Mass or Weight of the Frustum of a Polygon 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:

  • (n) Number of Polygon Sides
  • (b) Length of Sides on Top
  • (B) Length of Sides on Bottom
  • (h) Height of Pyramid
  • (mD) Density of Material (Default: 7,850 kg/m3 for steel)

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).

The formula for the mass of a regular pyramid frustum is:

`m = mD * n*h/12 * (b^2 + b*B + B^2) * cot(pi/n)`

where:

  • m = mass of the pyramid frustum
  • mD = density of material
  • h = height of pyramid
  • b = length of top sides
  • B = length of base sides
  • n = number of sides

Pyramid Calculators

A regular pyramid is a type of pyramid that has the following characteristics:

  1. 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.
  2. 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.
  3. 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.
  4. 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).

Mean Density Table

Common Mean Densities in Kilograms per Meter Cubed (kg/m3)

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 

Market-Ready Grains

 

Metals

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/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)

If you want to identify a material by its density, use the Density Within Range tool.