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127 LearnersLast updated on September 5, 2025
Volume of Irregular Prism
The volume of an irregular prism is the total space it occupies or the number of cubic units it can hold. An irregular prism is a 3D shape with non-uniform cross-sections along its length. To find the volume of an irregular prism, we multiply the area of its base by its height. In real life, kids relate to the volume of an irregular prism by thinking of things like a tent, a wedge-shaped doorstop, or certain architectural structures. In this topic, let’s learn about the volume of an irregular prism.
What is the volume of an irregular prism?
The volume of an irregular prism 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 base shape of the prism, and ‘Height’ is the perpendicular distance between the bases.
Volume of Irregular Prism Formula: An irregular prism is a 3-dimensional shape where the base can be any polygon. To calculate its volume, you multiply the area of the base by the height of the prism.
The formula for the volume of an irregular prism is given as follows: Volume = Base Area x Height
How to Derive the Volume of an Irregular Prism?
To derive the volume of an irregular prism, we use the concept of volume as the total space occupied by a 3D object. Since the base is irregular, its volume can be derived as follows:
The formula for the volume of any prism is:
Volume = Base Area x Height
For an irregular prism, the base can be any shape:
Calculate the area of the base
The volume of the prism will be, Volume = Base Area x Height
How to find the volume of an irregular prism?
The volume of an irregular prism is always expressed in cubic units, for example, cubic centimeters cm³, cubic meters m³. First, find the area of the base, then multiply it by the height to find the volume.
Let’s take a look at the formula for finding the volume of an irregular prism: Write down the formula
Volume = Base Area x Height
The base area is the area of one of the polygonal faces. The height is the perpendicular distance between the two bases.
Once we calculate the base area, substitute that value in the formula volume = Base Area x Height To find the volume, multiply the base area by the height.
Tips and Tricks for Calculating the Volume of Irregular Prism
Remember the formula: The formula for the volume of an irregular prism is simple: Volume = Base Area x Height
Break it down: The volume is how much space fits inside the prism. Simply calculate the area of the base and multiply it by the height.
Simplify the numbers: If the base area or height is a simple number, it is easy to multiply. For example, if the base area is 10 and the height is 5, the volume is 50. Check for base area If you are given the volume and need to find the base area, you can rearrange the formula. For example, if the volume is 100 and the height is 5, then the base area is 20.
Common Mistakes and How to Avoid Them in Volume of Irregular Prism
Making mistakes while learning the volume of an irregular prism is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of irregular prisms.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area is calculated by adding up the areas of all faces, but volume is calculated by multiplying the base area by the height. For example, the volume is Base Area x Height, not the sum of all face areas.
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 mistakenly think the formula for rectangular prisms applies to all prisms without considering the base shape.
Mistake 4
Ignoring the Base Shape
Underestimating the importance of the base shape in calculating area can lead to incorrect volume calculations. Always find the correct base area.
Mistake 5
Incorrectly calculating the base area
Some students calculate the volume by using an incorrect base area. Ensure you accurately determine the base area before using it in the volume formula.
Volume of Irregular Prism Examples
Problem 1
An irregular prism has a triangular base with an area of 10 cm² and a height of 5 cm. What is its volume?
The volume of the irregular prism is 50 cm³.
Explanation
To find the volume of the irregular prism, use the formula: V = Base Area x Height
Here, the base area is 10 cm² and the height is 5 cm, so: V = 10 x 5 = 50 cm³
Problem 2
A prism has a trapezoidal base with an area of 15 m² and a height of 8 m. Find its volume.
The volume of the prism is 120 m³.
Explanation
To find the volume of the prism, use the formula: V = Base Area x Height
Substitute the base area (15 m²) and height (8 m): V = 15 x 8 = 120 m³
Problem 3
The volume of an irregular prism is 200 cm³, and its height is 10 cm. What is the area of its base?
The base area of the prism is 20 cm².
Explanation
If you know the volume of the prism, and you need to find the base area, rearrange the formula:
Base Area = Volume / Height Base Area = 200 / 10 = 20 cm²
Problem 4
A prism has a pentagonal base with an area of 25 inches² and a height of 4 inches. Find its volume.
The volume of the prism is 100 inches³.
Explanation
Using the formula for volume: V = Base Area x Height
Substitute the base area (25 inches²) and height (4 inches): V = 25 x 4 = 100 inches³
Problem 5
You have a prism-shaped container with a hexagonal base area of 30 ft² and a height of 6 ft. How much space (in cubic feet) is available inside the container?
The container has a volume of 180 cubic feet.
Explanation
Using the formula for volume: V = Base Area x Height
Substitute the base area (30 ft²) and height (6 ft): V = 30 x 6 = 180 ft³
FAQs on Volume of Irregular Prism
1.Is the volume of an irregular prism the same as the surface area?
2.How do you find the volume if the base area and height are given?
3.What if I have the volume and need to find the base area?
4.Can the base area be irregular?
5.Can the height be a decimal or fraction?
Important Glossaries for Volume of Irregular Prism
- Base Area: The area of the polygonal face that serves as the base of the prism.
- Height: The perpendicular distance between the two bases of the prism.
- Volume: The amount of space enclosed within a 3D object. For an irregular prism, it 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 base area is in square centimeters (cm²) and height in centimeters (cm), the volume will be in cubic centimeters (cm³).
- Irregular Prism: A prism with non-uniform cross-sections along its length, meaning the base is not necessarily a rectangle or square.
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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
