Pyramid Frustum - Weight

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.

      mass = density ⋅ volume

A Right Square Pyramid has a four sided base where all four sides are equal and have equal angled corners (90^o), 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

Mean Density Table

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.

Pyramid Calculators

• Pyramid Geometries
• 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

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).