Volume Of Square Pyramid - Formula, Derivation, Examples - Cuemath

Volume of a Square Pyramid

What do we mean by the volume of a square pyramid and how do we define it? Volume is nothing but the space that an object occupies. A square pyramid is a three-dimensional geometric shape that has a square base and four triangular bases that are joined at a vertex. Thus, the volume of a pyramid refers to the space enclosed between its faces.

Let's learn how to find the volume of a square pyramid here with the help of few solved examples and practice questions.

1.	What Is the Volume of a Square Pyramid?
2.	Volume of a Square Pyramid Formula
3.	How to Find the Volume of a Square Pyramid?
4.	FAQs on Volume of a Square Pyramid

What Is the Volume of a Square Pyramid?

The volume of a square pyramid refers to the space enclosed between its five faces. The volume of a square pyramid is one-third of the product of the area of the base and the height of the pyramid. Thus, volume = (1/3) × (Base Area) × (Height). The volume of a square pyramid is the number of unit cubes that can fit into it and is represented in "cubic units". Commonly it's expressed as m3, cm3, in3, etc.

A square pyramid is a three-dimensional shape with five faces. A square pyramid is a polyhedron (pentahedron) that consists of a square base and four triangles connected to a vertex. Its base is a square and the side faces are triangles with a common vertex. A square pyramid has three components:

• The top point of the pyramid is called the apex.
• The bottom square of the pyramid is called the base.
• The triangular sides of the pyramid are called faces.

Examples of a square pyramid are the Great Pyramid of Giza, perfume bottles, etc

Let us learn more about the formula of the volume of a square pyramid.

Volume of a Square Pyramid Formula

The volume of a square pyramid can be easily found out by just knowing the base area and its height, and is given as:

Volume of a square pyramid = (1/3) Base Area × Height

Now, consider a regular square pyramid made of equilateral triangles of side 'b'.

The volume of a regular square pyramid can be given as:

Volume of a regular square pyramid = 1/3 × b2 × h where,

• b is the side of the base of the square pyramid, and,
• h is the height of the square pyramid

How To Find the Volume of a Square Pyramid?

As we learned in the previous section, the volume of a square pyramid could be found using (1/3) Base Area × Height. Thus, we follow the below steps to find the volume of a square pyramid.

• Step 1: Note the dimensions of the pyramid, like the base area and the height of the pyramid from the given data.
• Step 2: Multiply the area of the base by height and (1/3).
• Step 3: Represent the final answer with cubic units.

Now that we have learned about the volume of a square pyramid, let us understand it better using a few solved examples.