103 LearnersLast updated on July 17th, 2025
Volume of Prism
The volume of a prism is the total space it occupies or the number of cubic units it can hold. A prism is a 3D shape with two parallel, congruent bases connected by rectangular faces. To find the volume of a prism, we multiply the area of its base by its height. In real life, kids relate to the volume of a prism by thinking of things like a cereal box, a tent, or a fish tank. In this topic, let’s learn about the volume of prisms.
What is the volume of a prism?
The volume of a prism is the amount of space it occupies.
It is calculated by using the formula: Volume = Base Area × Height Where 'Base Area' is the area of the base of the prism, and 'Height' is the perpendicular distance between the two bases.
Volume of Prism Formula A prism is a 3-dimensional shape with two parallel bases.
To calculate its volume, you multiply the area of one base by the height of the prism.
The formula for the volume of a prism is given as follows: Volume = Base Area × Height
How to Derive the Volume of a Prism?
To derive the volume of a prism, we use the concept of volume as the total space occupied by a 3D object.
The volume can be derived as follows: The formula for the volume of any prism is: Volume = Base Area × Height For a rectangular prism, the base area can be calculated as Length × Width, and thus, Volume = Length × Width × Height
How to find the volume of a prism?
The volume of a prism is always expressed in cubic units, for example, cubic centimeters 'cm³', cubic meters 'm³'. Find the base area and multiply it by the height to find the volume.
Let’s take a look at the formula for finding the volume of a prism: Write down the formula Volume = Base Area × Height The base area is the area of one of the prism's bases.
Once we know the base area and the height, substitute those values into the formula Volume = Base Area × Height to find the volume.
Tips and Tricks for Calculating the Volume of Prism
Remember the formula: The formula for the volume of a prism is simple: Volume = Base Area × Height Break it down: The volume is how much space fits inside the prism.
Calculate the base area and multiply it by the height.
Simplify the numbers: If the dimensions are simple numbers like 2, 3, or 4, it is easy to calculate, for example, a rectangular base with sides 3 and 4 and height 5 gives a volume of 3 × 4 × 5 = 60.
Check for base area Ensure that you correctly calculate the area of the base based on its shape (e.g., rectangle, triangle).
Common Mistakes and How to Avoid Them in Volume of Prism
Making mistakes while learning the volume of the prism is common.
Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of 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 finding the area of all faces of the prism, but volume is calculated by multiplying the base area by the height.
For example, the volume is Base Area × 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 prism
Some kids use the formula for a specific type of prism (e.g., triangular prism) without considering the actual shape of the base.
Mistake 4
Confusing cubic volume with linear measurements
Thinking of volume in terms of linear measurements.
This happens when someone uses linear dimensions without understanding that volume relates to cubic measurements.
Mistake 5
Incorrectly calculating the base area
Some students calculate the base area incorrectly.
Ensure that the base area is calculated correctly, especially when the base is not a simple rectangle.
Volume of Prism Examples
Problem 1
A rectangular prism has a base area of 24 cm² and a height of 5 cm. What is its volume?
The volume of the prism is 120 cm³.
Explanation
To find the volume of a prism, use the formula: V = Base Area × Height Here, the base area is 24 cm² and the height is 5 cm, so: V = 24 × 5 = 120 cm³
Problem 2
A triangular prism has a base area of 15 m² and a height of 10 m. Find its volume.
The volume of the prism is 150 m³.
Explanation
To find the volume of a prism, use the formula: V = Base Area × Height Substitute the base area (15 m²) and height (10 m): V = 15 × 10 = 150 m³
Problem 3
The volume of a rectangular prism is 200 cm³, and its base area is 50 cm². What is the height of the prism?
The height of the prism is 4 cm.
Explanation
If you know the volume of the prism and the base area, you can find the height by rearranging the formula: Height = Volume / Base Area = 200 / 50 = 4 cm
Problem 4
A prism has a base area of 7.5 inches² and a height of 12 inches. Find its volume.
The volume of the prism is 90 inches³.
Explanation
Using the formula for volume: V = Base Area × Height Substitute the base area (7.5 inches²) and height (12 inches): V = 7.5 × 12 = 90 inches³
Problem 5
You have a prism-shaped box with a base area of 8 ft² and a height of 6 ft. How much space (in cubic feet) is available inside the box?
The box has a volume of 48 cubic feet.
Explanation
Using the formula for volume: V = Base Area × Height Substitute the base area (8 ft²) and height (6 ft): V = 8 × 6 = 48 ft³
FAQs on Volume of Prism
1.Is the volume of a prism the same as the surface area?
2.How do you find the volume if the base area is given?
3.What if I have the volume and need to find the height?
4.Can the base area be a decimal or fraction?
5.Are all prisms calculated the same way?
Important Glossaries for Volume of Prism
- Base Area: The area of the base of the prism, which determines one part of the volume calculation.
- Height: The perpendicular distance between the bases of the prism. Volume: The amount of space enclosed within a 3D object, expressed in cubic units.
- Prism: A solid object with two identical ends and flat sides. The sides are parallelograms, and the cross-section is the same all along its length.
- Cubic Units: The units of measurement used for volume. If the dimensions are 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
