108 LearnersLast updated on July 11th, 2025
Volume of Cuboid with Square Base
The volume of a cuboid with a square base is the total space it occupies or the number of cubic units it can hold. This type of cuboid has a square base and a height that may differ from the base side length. To find the volume of a cuboid with a square base, we multiply the area of the square base by its height. In real life, kids might relate the volume of such a shape to things like a box of cereal or a rectangular aquarium. In this topic, let’s learn about the volume of a cuboid with a square base.
What is the volume of a cuboid with a square base?
The volume of a cuboid with a square base is the amount of space it occupies. It is calculated by using the formula: Volume = base_area x height
Where ‘base_area’ is the area of the square base (side x side), and 'height' is the perpendicular distance from the base to the top face. Volume of Cuboid with Square Base Formula
A cuboid with a square base is a 3-dimensional shape where the length and width are equal, forming a square, and the height is a separate measurement.
To calculate its volume, you multiply the area of the square base by the height. The formula for the volume of a cuboid with a square base is: Volume = side² x height
How to Derive the Volume of a Cuboid with a Square Base?
To derive the volume of a cuboid with a square base, we use the concept of volume as the total space occupied by a 3D object.
Since the base is square, its area is side², and the height is independent.
The formula for the volume of any rectangular prism is: Volume = Length x Width x Height
For a cuboid with a square base: Length = Width = side
The volume of a cuboid with a square base will be, Volume = side x side x height
Volume = side² x height
How to find the volume of a cuboid with a square base?
The volume of a cuboid with a square base is always expressed in cubic units, for example, cubic centimeters cm³, cubic meters m³.
To find the volume, calculate the area of the base (side x side) and multiply it by the height.
Let’s take a look at the formula for finding the volume of a cuboid with a square base:
Write down the formula Volume = side² x height The side is the length of one edge of the square base. The side length of the base is the length of one of its edges, while the height is the perpendicular distance to the top face.
Once we know the side length and height, substitute those values into the formula: Volume = side² x height Calculate the base area and multiply it by the height to find the volume.
Tips and Tricks for Calculating the Volume of a Cuboid with Square Base
Remember the formula: The formula for the volume of a cuboid with a square base is: Volume = side² x height
Break it down: The volume is how much space fits inside the cuboid. Calculate the area of the square base and multiply it by the height.
Simplify the numbers: If the side length or height is a simple number like 2, 3, or 4, it is easy to calculate the volume. For instance, if side = 2 and height = 3, then volume = 2² x 3 = 12.
Check for square roots If you are given the volume and need to find the side length, you may need to find the square root of the base area or solve for the height.
Common Mistakes and How to Avoid Them in Volume of Cuboid with Square Base
Making mistakes while learning the volume of a cuboid with a square base is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of cuboids with square bases.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area involves all faces of the cuboid, whereas volume is calculated by multiplying the base area by the height. For example, the volume is side² x height, not involving the surface area formula.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the perimeter of the base instead of the volume formula. Volume is the space inside the cuboid, 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 x width x height) without realizing that for a square base, length and width are equal.
Mistake 4
Confusing cubic volume with linear volume
Thinking of volume in terms of linear measurements. This happens when someone focuses on side length without considering the height for volume calculations.
Mistake 5
Incorrectly calculating the side length
Some students calculate the given volume without correctly solving for the side length or height. Remember to find the square root of the base area if required.
Volume of Cuboid with Square Base Examples
Problem 1
A cuboid has a square base with a side length of 5 cm and a height of 10 cm. What is its volume?
The volume of the cuboid is 250 cm³.
Explanation
To find the volume of a cuboid with a square base, use the formula: V = side² x height
Here, the side length is 5 cm and the height is 10 cm,
so: V = 5² x 10 = 25 x 10 = 250 cm³
Problem 2
A cuboid with a square base has a side length of 7 m and a height of 5 m. Find its volume.
The volume of the cuboid is 245 m³.
Explanation
To find the volume of a cuboid with a square base, use the formula: V = side² x height
Substitute the side length (7 m) and height (5 m): V = 7² x 5 = 49 x 5 = 245 m³
Problem 3
The volume of a cuboid with a square base is 500 cm³, and its height is 10 cm. What is the side length of the base?
The side length of the base is 5√2 cm.
Explanation
If you know the volume of the cuboid and need to find the side length, rearrange the formula:
V = side² x height 500 = side² x 10 side² = 50 side = √50 = 5√2 cm
Problem 4
A cuboid has a square base with a side length of 3.5 inches and a height of 4 inches. Find its volume.
The volume of the cuboid is 49 inches³.
Explanation
Using the formula for volume: V = side² x height Substitute the side length 3.5 inches and height 4 inches:
V = (3.5)² x 4 = 12.25 x 4 = 49 inches³
Problem 5
You have a cuboid-shaped box with a square base side length of 2 feet and a height of 6 feet. How much space (in cubic feet) is available inside the box?
The box has a volume of 24 cubic feet.
Explanation
Using the formula for volume: V = side² x height
Substitute the side length 2 feet and height 6 feet: V = 2² x 6 = 4 x 6 = 24 ft³
FAQs on Volume of Cuboid with Square Base
1.Is the volume of a cuboid with a square base 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?
4.Can the side length or height be a decimal or fraction?
5.Can the volume formula be used for any cuboid?
Important Glossaries for Volume of Cuboid with Square Base
- Side: The length of one of the edges of the square base of the cuboid.
- Height: The perpendicular distance from the base to the top face of the cuboid.
- Volume: The amount of space enclosed within a 3D object. In the case of a cuboid with a square base, the volume is calculated by multiplying the base area by the height. It is expressed in cubic units (e.g., cm³, m³).
- Square base: A base that is a square, meaning the length and width are equal.
- 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
