102 LearnersLast updated on 5 September 2025
Volume of Square Prism
The volume of a square prism is the total space it occupies or the number of cubic units it can hold. A square prism is a 3D shape with two square bases and rectangular lateral faces. To find the volume of a square prism, we multiply the area of its base by its height. In real life, kids might relate to the volume of a square prism by thinking of objects like a box or a tower. In this topic, let’s learn about the volume of a square prism.
What is the volume of a square prism?
The volume of a square prism is the amount of space it occupies. It is calculated by using the formula:
Volume = base area × height
Where the base area is the area of the square base of the prism.
Volume of Square Prism Formula : A square prism has a square base, so to calculate its volume, you multiply the area of its base by its height.
The formula for the volume of a square prism is given as follows: Volume = side² × height
How to Derive the Volume of a Square Prism?
To derive the volume of a square prism, we use the concept of volume as the total space occupied by a 3D object.
Since a square prism has a square base, its volume can be derived as follows: The formula for the volume of any prism is:
Volume = Base Area × Height
For a square prism: Base Area = side² (since the base is a square with equal sides)
The volume of a square prism will be, Volume = side² × height
How to find the volume of a square prism?
The volume of a square prism is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³). Multiply the area of the square base by the height to find the volume.
Let’s take a look at the formula for finding the volume of a square prism:
Write down the formula Volume = side² × height
The side is the length of one edge of the square base.
Once we know the length of the side and the height, substitute those values into the formula Volume = side² × height.
Tips and Tricks for Calculating the Volume of Square Prism
Remember the formula: The formula for the volume of a square prism is simple: Volume = side² × height
Break it down: The volume is how much space fits inside the prism. Multiply the side length squared by the height.
Simplify the numbers: If the side length is a simple number like 2, 3, or 4, it is easy to calculate the base area. For example, if side = 3, then side² = 9.
Check for square roots: If you are given the base area and need to find the side length, you can find the square root. For example, if the base area is 16, then the side length is 4.
Common Mistakes and How to Avoid Them in Volume of Square Prism
Making mistakes while learning the volume of a square prism is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of square prisms.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area involves calculating the area of all faces, but volume is calculated by multiplying the base area by the height. For example, the volume is side² × height, not the total area of all faces.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the prism’s perimeter instead of the volume formula. Volume is the space inside the prism, whereas perimeter refers to the total length around the edges of a 2D shape. Do not mix them up.
Mistake 3
Using the wrong formula for rectangular prisms
Some kids use the formula for the volume of a general rectangular prism (length × width × height) instead of the specific formula for a square prism.
Mistake 4
Confusing cubic volume with linear measurements
Thinking of volume in terms of linear measurements. This happens when someone uses the side length (which is a linear measurement) instead of understanding that volume relates to cubic measurements.
Mistake 5
Incorrectly calculating the side length
Some students calculate the given base area incorrectly when solving for the side length. For example, if the base area is given, and they need to find the side, they might forget to take the square root of the base area.
Volume of Square Prism Examples
Problem 1
A square prism has a base side length of 4 cm and a height of 10 cm. What is its volume?
The volume of the square prism is 160 cm³.
Explanation
To find the volume of a square prism, use the formula: V = side² × height
Here, the side length is 4 cm and the height is 10 cm, so: V = 4² × 10 = 16 × 10 = 160 cm³
Problem 2
A square prism has a base side length of 5 m and a height of 7 m. Find its volume.
The volume of the square prism is 175 m³.
Explanation
To find the volume of a square prism, use the formula: V = side² × height
Substitute the side length (5 m) and height (7 m):
V = 5² × 7 = 25 × 7 = 175 m³
Problem 3
The volume of a square prism is 200 cm³, and its height is 8 cm. What is the side length of the base?
The side length of the base is 5 cm.
Explanation
If you know the volume of the square prism and the height, and you need to find the side length, you’ll rearrange the formula: Base Area = Volume / Height
side² = 200 / 8 = 25
Side length = √25 = 5 cm
Problem 4
A square prism has a base side length of 3 inches and a height of 6 inches. Find its volume.
The volume of the square prism is 54 inches³.
Explanation
Using the formula for volume: V = side² × height
Substitute the side length 3 inches and height 6 inches: V = 3² × 6 = 9 × 6 = 54 inches³
Problem 5
You have a square prism with a base side length of 2 feet and a height of 5 feet. How much space (in cubic feet) is available inside the prism?
The prism has a volume of 20 cubic feet.
Explanation
Using the formula for volume: V = side² × height
Substitute the side length 2 feet and height 5 feet: V = 2² × 5 = 4 × 5 = 20 ft³
FAQs on Volume of Square Prism
1.Is the volume of a square prism the same as the surface area?
2.How do you find the volume if the side length and height are given?
3.What if I have the volume and need to find the side length of the base?
4.Can the side length be a decimal or fraction?
5.Is the volume of a square prism the same as the surface area?
Important Glossaries for Volume of Square Prism
- Side: The length of one of the square base’s edges.
- Base Area: The area of the square base of the prism, calculated as side².
- Height: The perpendicular distance between the two square bases of the prism.
- Volume: The amount of space enclosed within a 3D object. In the case of a square prism, the volume is calculated by multiplying the base area by the height. It is expressed in cubic units (e.g., cm³, m³).
- Cubic Units: The units of measurement used for volume. If the side length is in centimeters (cm), the volume will be in cubic centimeters (cm³); if in meters, it will be in cubic meters (m³).
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
