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113 LearnersLast updated on September 5, 2025
Volume of Octagonal Prism
The volume of an octagonal prism is the total space it occupies or the number of cubic units it can hold. An octagonal prism is a 3D shape with two parallel octagonal bases and rectangular faces connecting these bases. To find the volume of an octagonal prism, we multiply the area of the octagonal base by the height of the prism. In real life, the concept of the volume of an octagonal prism can be related to structures like towers or columns with octagonal bases. In this topic, let’s learn about the volume of an octagonal prism.
What is the volume of the octagonal prism?
The volume of an octagonal 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 octagonal base, and 'Height' is the distance between the two bases.
Volume of Octagonal Prism Formula : An octagonal prism is a 3-dimensional shape with two octagonal bases. To calculate its volume, you find the area of the octagonal base and multiply it by the height of the prism.
The formula for the volume of an octagonal prism is given as follows: Volume = Base Area × Height
How to Derive the Volume of an Octagonal Prism?
To derive the volume of an octagonal 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 a prism is: Volume = Base Area × Height
For an octagonal prism:
Calculate the area of the octagonal base using its specific formula, then multiply by the height of the prism.
Volume = Base Area × Height
How to find the volume of an octagonal prism?
The volume of an octagonal prism is always expressed in cubic units, for example, cubic centimeters (cm³) or cubic meters (m³). Calculate the area of the octagonal 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 octagonal prism:
Write down the formula Volume = Base Area × Height Find the area of the octagonal base using its formula.
Once you have the base area and the height, substitute these values into the formula
Volume = Base Area × Height.
Tips and Tricks for Calculating the Volume of an Octagonal Prism
- Remember the formula: The formula for the volume of an octagonal prism is: Volume = Base Area × Height
- Break it down: The volume is how much space fits inside the prism. First, calculate the base area, then multiply by the height.
- Simplify the numbers: Ensure you correctly calculate the base area as it involves more complex calculations than simple shapes.
- Check your units: Always make sure that the base area and height are in compatible units before multiplying.
Common Mistakes and How to Avoid Them in Volume of Octagonal Prism
Making mistakes while learning the volume of the octagonal prism is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of octagonal prisms.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area involves all the faces of the prism, while volume is calculated by multiplying the base area by the height.
Mistake 2
Using the Wrong Formula for Base Area
Students often use incorrect formulas for calculating the area of the octagonal base. Make sure to use the correct formula specific to an octagon.
Mistake 3
Incorrectly Calculating Base Area
Errors may occur when calculating the base area due to the complexity of the formula for an octagon. Double-check calculations or use a calculator.
Mistake 4
Ignoring the Height of the Prism
Some might forget to include the height in the volume calculation, resulting in incorrect values. Always multiply the base area by the height.
Mistake 5
Misaligning Units
Ensure that the base area and height are measured in compatible units before multiplying to avoid errors in the final volume calculation.
Volume of Octagonal Prism Examples
Problem 1
An octagonal prism has a base area of 50 cm² and a height of 10 cm. What is its volume?
The volume of the octagonal prism is 500 cm³.
Explanation
To find the volume of the octagonal prism, use the formula:
V = Base Area × Height
Here, the base area is 50 cm² and the height is 10 cm, so: V = 50 × 10 = 500 cm³
Problem 2
An octagonal prism has a base area of 30 m² and a height of 5 m. Find its volume.
The volume of the octagonal prism is 150 m³.
Explanation
To find the volume of the octagonal prism, use the formula:
V = Base Area × Height
Substitute the base area (30 m²) and height (5 m): V = 30 × 5 = 150 m³
Problem 3
The volume of an octagonal prism is 960 cm³, and its base area is 80 cm². What is the height of the prism?
The height of the octagonal prism is 12 cm.
Explanation
To find the height of the prism when the volume and base area are known, use the formula:
Height = Volume / Base Area
Height = 960 / 80 = 12 cm
Problem 4
An octagonal prism has a base area of 15 square inches and a height of 4 inches. Find its volume.
The volume of the octagonal prism is 60 inches³.
Explanation
Using the formula for volume: V = Base Area × Height
Substitute the base area 15 square inches and height 4 inches:
V = 15 × 4 = 60 inches³
Problem 5
You have an octagonal prism with a base area of 25 ft² and a height of 8 ft. How much space (in cubic feet) is available inside the prism?
The prism has a volume of 200 cubic feet.
Explanation
Using the formula for volume: V = Base Area × Height
Substitute the base area 25 ft² and height 8 ft:
V = 25 × 8 = 200 ft³
FAQs on Volume of Octagonal Prism
1.Is the volume of an octagonal 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 height?
4.Can the base area be a decimal or fraction?
5.What is the key difference between volume and surface area in an octagonal prism?
Important Glossaries for Volume of Octagonal Prism
- Base Area: The area of one of the octagonal bases of the prism, crucial for calculating volume.
- Volume: The amount of space enclosed within a 3D object, calculated by multiplying the base area by the height.
- 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 meters (m²), and the height is in meters (m), the volume will be in cubic meters (m³).
- Octagonal Base: The eight-sided polygon that forms the base of the prism.
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
