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108 LearnersLast updated on September 5, 2025
Volume of Pentagonal Prism
The volume of a pentagonal prism is the total space it occupies or the number of cubic units it can hold. A pentagonal prism is a 3D shape with two parallel pentagonal bases and rectangular lateral faces. To find the volume of a pentagonal prism, we multiply the area of the pentagonal base by the height of the prism. In real life, kids relate to the volume of a pentagonal prism by thinking of structures like certain types of buildings or architectural models. In this topic, let’s learn about the volume of the pentagonal prism.
What is the volume of the pentagonal prism?
The volume of a pentagonal 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 pentagonal base, and 'Height' is the perpendicular distance between the two bases.
Volume of Pentagonal Prism Formula: A pentagonal prism is a 3-dimensional shape with two congruent pentagonal bases. To calculate its volume, you multiply the area of one pentagonal base by the height of the prism.
The formula for the volume of a pentagonal prism is given as follows: Volume = Base Area × Height
How to Derive the Volume of a Pentagonal Prism?
To derive the volume of a pentagonal prism, we use the concept of volume as the total space occupied by a 3D object. Since a pentagonal prism has a pentagonal base, its volume can be derived as follows:
The formula for the volume of any prism is: Volume = Base Area × Height
For a pentagonal prism: Base Area = Area of the pentagon
The volume of a pentagonal prism will be, Volume = (Area of pentagon) × Height
How to find the volume of a pentagonal prism?
The volume of a pentagonal prism is always expressed in cubic units, for example, cubic centimeters 'cm³', cubic meters 'm³'. Calculate the area of the pentagonal base, and multiply it by the height, to find the volume.
Let’s take a look at the formula for finding the volume of a pentagonal prism:
Write down the formula Volume = Base Area × Height
The 'Base Area' is the area of the pentagonal base, which can be calculated using a specific formula for the area of a pentagon if its side length is known. Once we know the base area and the height, substitute those values into the formula to find the volume:
Volume = (Area of pentagon) × Height.
Tips and Tricks for Calculating the Volume of Pentagonal Prism
Remember the formula: The formula for the volume of a pentagonal prism is: Volume = Base Area × Height
Break it down: The volume is how much space fits inside the prism. Calculate the base area of the pentagon first, and then multiply by the height.
Simplify the numbers: If the side length of the pentagon and the height are simple numbers, it is easier to calculate.
Check for accuracy: Ensure that the base area is calculated correctly for accurate volume computation.
Common Mistakes and How to Avoid Them in Volume of Pentagonal Prism
Making mistakes while learning the volume of the pentagonal prism is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of pentagonal 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 Base Area × 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 different prisms
Some kids use the formula for the volume of other prisms (like a rectangular prism) instead of the pentagonal prism formula.
Mistake 4
Confusing base area with lateral area
Thinking of the base area in terms of lateral measurements. This happens when someone uses the lateral face area instead of understanding that the volume relates to the base area of the pentagon.
Mistake 5
Incorrectly calculating the base area
Some students calculate the given volume with solving for the base area. For example, if the volume is given, and they need to find the base area, they might forget to divide the volume by the height.
Volume of Pentagonal Prism Examples
Problem 1
A pentagonal prism has a base area of 20 cm² and a height of 10 cm. What is its volume?
The volume of the pentagonal prism is 200 cm³.
Explanation
To find the volume of a pentagonal prism, use the formula: V = Base Area × Height
Here, the base area is 20 cm² and the height is 10 cm, so: V = 20 × 10 = 200 cm³
Problem 2
A pentagonal prism has a base area of 15 m² and a height of 12 m. Find its volume.
The volume of the pentagonal prism is 180 m³.
Explanation
To find the volume of a pentagonal prism, use the formula: V = Base Area × Height
Substitute the base area (15 m²) and height (12 m): V = 15 × 12 = 180 m³
Problem 3
The volume of a pentagonal prism is 300 cm³, and its height is 5 cm. What is the base area of the prism?
The base area of the pentagonal prism is 60 cm².
Explanation
If you know the volume of the prism and need to find the base area, you divide the volume by the height.
The formula for the base area A is: A = Volume / Height = 300 / 5 = 60 cm²
Problem 4
A pentagonal prism has a base area of 8 square inches and a height of 7 inches. Find its volume.
The volume of the pentagonal prism is 56 inches³.
Explanation
Using the formula for volume: V = Base Area × Height
Substitute the base area (8 square inches) and height (7 inches): V = 8 × 7 = 56 inches³
Problem 5
You have a pentagonal prism with a base area of 25 square feet and a height of 4 feet. How much space (in cubic feet) is available inside the prism?
The prism has a volume of 100 cubic feet.
Explanation
Using the formula for volume: V = Base Area × Height
Substitute the base area (25 square feet) and height (4 feet): V = 25 × 4 = 100 ft³
FAQs on Volume of Pentagonal Prism
1.Is the volume of a pentagonal 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 height be a decimal or fraction?
5.Is the volume of a pentagonal prism the same as the surface area?
Important Glossaries for Volume of Pentagonal Prism
- Base Area: The area of the pentagonal base of the prism.
- Volume: The amount of space enclosed within a 3D object, calculated by multiplying the base area by the height for a pentagonal prism.
- Height: The perpendicular distance between the two bases of the prism.
- Cubic Units: The units of measurement used for volume. If the base area is in square centimeters (cm²), and the height is in centimeters (cm), the volume will be in cubic centimeters (cm³).
- Pentagonal Prism: A 3-dimensional shape with two parallel pentagonal bases and rectangular lateral faces.
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
