Frustum

vCalc Reviewed
Calculator / Last modified by KurtHeckman on 2016/02/08 14:57
Volumes
Cone Volume
Cored cone volume
Pyramid Volume
Bottle - volume
Cone mass
Cored cone mass
Pyramid mass
Bottle mass
Mean Density Table Lookup
Cone - Frustum Surface Area
Cone - Frustum Surface Area (total)
Cone - Frustum Surface Area 2
Pyramid Frustum (polygon base) - surface area
Bottle - surface area

The Frustum Calculator provides equations to calculate volume, mass, and surface area of common frustums frustrum - l.jpg Cone frustum  , including cones, bottles, pyramids, and cored cones.  A frustum is a section of a solid that is produced by "cutting" it between two parallel planes.
cone-frustum-cored.pngCored Frustum (aka chamfer)

Description

The Frustum calculator provides equations related to Frustums (see definition below).  The equations include:

  • Volume: The Volume tab of the calculator provides calculations of total volume from given dimensions (see diagrams).
  • Surface Area: The Surface Area tab provides calculations of surface area, some including the bases (top and bottom) and some not.    pyramid frustum - polyon base.png Frustum of a polygon pyramid 
  • Mass: The Mass tab provides calculations of total volume given input dimensions and a specified mean density.   The calculator button labeled "Common Mean Densities" offers numerous mean densities of common materials such as iron, air, sea water, and concrete which may be used as input to the mass equations.

 (Common Mean Densities)For the mass equations, one can use the common mean densities formula to look up the mean density of common substances and then use the resulting value as input to the mass equation. The Mean Density Table Lookup button provides the mean density of hundreds (650+) of substances from gases, to metals, woods, foods, liquids and much more.  The results are given in `"kg"/m^3` which is the default input units for the mass calculation.

The result of the mass equation can then be used in the equations for the moments of inertia.

Frustum

In geometry, a frustum (plural: frusta or frustums) is the portion of a solid (normally a cone or pyramid) that lies between two parallel planes cutting it.

The term is commonly used in computer graphics to describe the three-dimensional region which is visible on the screen, the "viewing frustum", which is formed by a clipped pyramid; in particular, frustum culling is a method of hidden surface determination.

In the aerospace industry, frustum is the common term for the fairing between two stages of a multistage rocket (such as the Saturn V), which is shaped like a truncated cone.

In geology, the caldera of a volcano can be approximated as an inverted conic frustum. The volume of a bucket can also be calculated as an inverted conic frustum. By combining a frustum with a cylinder, one can calculate the metrics of a bottle.

bottle.png Conic frustum on top of cylinder (aka bottle) 

See Also

References

  • Wikipedia - http://en.wikipedia.org/wiki/Frustum