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:
- (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
| Common Mean Densities |
| Metals
|
| Fluids
|
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
The mean density(mD) of over 500 materials can found by clicking HERE.