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.

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.

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

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.

What Is Volume of Square Pyramid?

The volume of a square pyramid is the space enclosed by the solid shape in a three-dimensional plane. A square pyramid is a three-dimensional shape with five faces. Its base is a square and the side faces are triangles with a common vertex.

How Do You Find the Volume of a Square Pyramid?

The volume of a square pyramid can be easily found by just knowing the base area and its height. We can directly apply the volume of a square pyramid formula given the base and height as, Volume = 1/3 × Base Area × Height.

What Is the Volume of a Regular Square Pyramid?

Volume of square pyramid is the space or region enclosed by a regular square pyramid in a three-dimensional plane. The formula to calculate the volume of a regular square pyramid is given as, Regular square pyramid volume:1/3 × a² × h, where 'a' is the side of the square faces and 'h' is the height of the pyramid.

What Units Are Used With the Volume of the Square Pyramid?

The volume of a square pyramid is expressed in cubic units. Generally, units like cubic meters (m³), cubic centimeters (cm³), liters (l), etc are the most common units used with the volume of the square pyramid.

How Do You Find the Volume of Pyramid and Prisms?

The volume of the prism can be calculated using the base area and height. The formula for the volume of a prism is equal to the base area × height of the pyramid. While the volume of a pyramid can be calculated as, 1/3 × Base Area × Height.

What Is the Formula for Finding the Volume of a Square Pyramid?

The volume of a square pyramid is found using the formula using the base area and height given as, V = 1/3 × Base Area × Height. For a regular pyramid, we can apply the following formula, given the side of square face and height,
1/3 × a² × h, where 'a' is the side of the square faces and 'h' is the height of the pyramid.

How to Find the Height of a Square Pyramid When Given the Volume?

To find the height of a square pyramid using the volume, we can apply the volume of a pyramid formula, substitute the given values and solve for the missing height,
Volume of square pyramid = Volume = 1/3 × Base Area × Height

How Does the Volume of a Square Pyramid Relate to the Volume of a Square Prism?

Given a prism and a pyramid with congruent bases and the same height, if we put the pyramid inside the prism, their bases overlap exactly. Since both the shapes have the same height, the top of the pyramid will touch the top of the prism. Thus, the pyramid fits completely in the given pyramid. The relation between the volume of a pyramid and a prism can be given as,
Volume of a square pyramid = (1/3) Volume of a square prism