Volume of Polygon Base Pyramid Frustum

Last modified by

KurtHeckman

on

Aug 28, 2024, 7:53:41 PM

Created by

KurtHeckman

on

Jul 15, 2014, 5:33:54 PM

$V = "n" * "h" /12 * ( "b" ^2 + "b" * "B" + "B" ^2) * cot(pi/ "n" )$

$(n) "Number of Sides"$

$(b) "Length of Top Sides"$

$(B) "Length of Bottom Sides"$

$(h) "Height of Frustum"$

The Math / Science

The top and base polygons are regular polygons with equal length sides and angles. The polygons are defined by the number of sides (n) and the equal side lengths of b and B of the two polygons respectively (see diagram).

The formula for the volume of a polygon pyramid frustum is:

V = n⋅h/12⋅(b²+b⋅B+B²)⋅cot(π/n)

where:

V is the volume of the polygon pyramid frustum
n is the number of sides of the polygon
b is the length of the sides on the top polygon
B is the length of the sides on the bottom polygon

Pyramid Calculators

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

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.
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.
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.
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).

Volume is a three dimensional measurement of the amount of space taken up by an object. Volume units are cubic measurements for solid objects such as cubic inches and cubic meters. Fluids have separate volume units such as liters, fluid ounces, cups, gallons, and barrel.

The volume of an object can measured by the liquid it displaces or be calculated by measuring its dimensions and applying those dimensions to a formula describing its shape. Many such calculations are available in the following list of calculators.

In many cases, the calculators are for a column with a geometric shaped base and vertical sides. One basic formula for volume is area times a Height when the volume has vertical sides.