The Volume of a Pyramid Formula

The amount of space that a pyramid takes up, also known as its volume, may also be described by the number of unit cubes that are able to fit inside of it.

A pyramid is a kind of polyhedron because each of its faces is composed of a different kind of polygon. Named after the shape of their bases, the various types of pyramids include triangular pyramids, square pyramids, rectangular pyramids, pentagonal pyramids, etc. 

For example, a pyramid is referred to as a square pyramid if its base is in the shape of a square. Other examples include rectangular pyramids, pentagonal pyramids, and rectangular pyramids. In a pyramid, each of the side faces is in the shape of a triangle, and one side of each triangle is joined to one of the sides of the base.

The amount of space that is encompassed by the faces of a pyramid is referred to as its volume. If the bases of the pyramid and prism are congruent and the heights of the pyramid and prism are also the same, then the volume of any pyramid is always one-third of the volume of a prism. This means that three pyramids of the same type can be arranged to form a prism of the same type if the heights of the pyramid and the prism are the same and their bases are congruent.

The volume of a Pyramid Formula

Let us take into consideration a pyramid and a prism, both of which have a height “h” and a base area denoted by “B.” It is common knowledge that the volume of a prism may be calculated by multiplying the base by the height of the prism. Therefore, the volume of the prism is denoted by the symbol Bh. As was said in the previous part of this article, the volume of a pyramid is 1/3 of the volume of the prism that it corresponds to (i.e., their bases and heights are congruent). Thus,

The volume of the pyramid = (1/3) (Bh), where

• B = Area pyramid’s base
• h = Height 

Solved Examples

Example 1: The base of the Cheops pyramid in Egypt is about 755 feet by 755 feet, and its height is around 480 feet. Calculate its volume.

Solution:

B = 755 × 755 = 570,025 sq. feet.

The height, h = 480 ft.

Using volume formula,

Volume, V = (1/3) (Bh)

V = (1/3) × 570025 × 480

V = 91,204,000 cubic feet.