109 LearnersLast updated on July 11th, 2025
Volume of Oblique Prism
The volume of an oblique prism is the total space it occupies or the number of cubic units it can hold. An oblique prism is a type of prism in which the sides lean over the base, and the lateral faces are parallelograms. To find the volume of an oblique prism, we multiply the area of the base by the height of the prism. In real life, you might relate to the volume of an oblique prism by thinking of objects like a slanted glass or a leaning tower. In this topic, let’s learn about the volume of an oblique prism.
What is the volume of the oblique prism?
The volume of an oblique prism is the amount of space it occupies. It is calculated by using the formula: Volume = Base Area × Height
Where the base area is the area of the base of the prism, and the height is the perpendicular distance between the bases.
Volume of Oblique Prism Formula An oblique prism is a 3-dimensional shape where the sides are not perpendicular to the base.
To calculate its volume, you multiply the area of the base by the height. The formula for the volume of an oblique prism is given as follows: Volume = Base Area × Height
How to Derive the Volume of an Oblique Prism?
To derive the volume of an oblique prism, we consider 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 an oblique prism, even though the sides are slanted, the height is measured as the perpendicular distance between the base and the top face.
Therefore, the volume of an oblique prism will be, Volume = Base Area × Height
How to find the volume of an oblique prism?
The volume of an oblique prism is always expressed in cubic units, for example, cubic centimeters (cm³) or cubic meters (m³). Calculate 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 an oblique prism: Write down the formula Volume = Base Area × Height
The base area is the area of the prism's base. The height is the perpendicular distance between the two bases.
Once we know the base area and the height, substitute those values in the formula Volume = Base Area × Height to find the volume.
Tips and Tricks for Calculating the Volume of an Oblique Prism
Remember the formula: The formula for the volume of an oblique prism is simple: Volume = Base Area × Height
Break it down: The volume is how much space fits inside the prism. Calculate the area of the base and multiply it by the height.
Simplify the numbers: If the base has a simple shape like a rectangle or triangle, calculate its area first.
Check for base area: Ensure you accurately calculate the base area, especially if the base is a complex shape.
Volume of Oblique Prism Examples
Problem 1
An oblique prism has a triangular base with an area of 30 cm² and a height of 10 cm. What is its volume?
The volume of the oblique prism is 300 cm³.
Explanation
To find the volume of an oblique prism, use the formula: V = Base Area × Height
Here, the base area is 30 cm² and the height is 10 cm,
so: V = 30 × 10 = 300 cm³
Problem 2
An oblique prism has a rectangular base that is 5 m by 3 m, and a height of 12 m. Find its volume.
The volume of the oblique prism is 180 m³.
Explanation
To find the volume of an oblique prism, use the formula: V = Base Area × Height
The base area is 5 m × 3 m = 15 m².
Substitute the base area and height (12 m): V = 15 × 12 = 180 m³
Problem 3
The volume of an oblique prism is 400 cm³ with a base area of 50 cm². What is the height of the prism?
The height of the prism is 8 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 Height = 400 / 50 = 8 cm
Problem 4
An oblique prism has a hexagonal base with an area of 100 inches² and a height of 15 inches. Find its volume.
The volume of the oblique prism is 1500 inches³.
Explanation
Using the formula for volume: V = Base Area × Height
Substitute the base area (100 inches²) and height (15 inches):
V = 100 × 15 = 1500 inches³
Problem 5
You have an oblique prism with a base area of 25 ft² and a height of 5 ft. How much space (in cubic feet) is available inside the prism?
The prism has a volume of 125 cubic feet.
Explanation
Using the formula for volume: V = Base Area × Height Substitute the base area (25 ft²) and height (5 ft):
V = 25 × 5 = 125 ft³
FAQs on Volume of Oblique Prism
1.Is the volume of an oblique 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 complex shape like a polygon?
5.Is the volume of an oblique prism the same as the lateral area?
Important Glossaries for Volume of Oblique Prism
- Base Area: The area of the base of the prism. It is crucial for calculating the volume.
- Height: The perpendicular distance between the two bases of the prism.
- Volume: The amount of space enclosed within a 3D object, calculated by multiplying base area by 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).
- Oblique Prism: A type of prism where the lateral faces are not perpendicular to the base and are parallelograms.
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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
