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116 LearnersLast updated on September 5, 2025
Volume of Oblique Cylinder
The volume of an oblique cylinder is the total space it occupies or the number of cubic units it can hold. An oblique cylinder differs from a right cylinder in that its sides are not perpendicular to its bases. To find the volume of an oblique cylinder, we use the same formula as for a right cylinder: multiply the area of the base by the height. In real life, kids relate to the volume of an oblique cylinder by thinking of things like a slanted can or a tilted glass. In this topic, let’s learn about the volume of the oblique cylinder.
What is the volume of the oblique cylinder?
The volume of an oblique cylinder is the amount of space it occupies. It is calculated by using the formula:
Volume = πr²h Where ‘r’ is the radius of the base and ‘h’ is the height of the cylinder.
Volume of Oblique Cylinder Formula: An oblique cylinder is a 3-dimensional shape where the sides are slanted, but the bases are parallel and circular.
To calculate its volume, you multiply the area of the base (πr²) by the height (h).
The formula for the volume of an oblique cylinder is given as follows: Volume = πr²h
How to Derive the Volume of an Oblique Cylinder?
To derive the volume of an oblique cylinder, we use the concept of volume as the total space occupied by a 3D object.
The formula for the volume of any cylinder, including an oblique cylinder, is:
Volume = Base Area x Height
For a cylinder: Base Area = πr² Height = h (the perpendicular distance between the bases)
The volume of an oblique cylinder will be, Volume = πr²h
How to find the volume of an oblique cylinder?
The volume of an oblique cylinder is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³).
Calculate the area of the base using πr², 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 cylinder:
Write down the formula Volume = πr²h
The radius is the distance from the center to any point on the edge of the base. The height of an oblique cylinder is the perpendicular distance between the bases.
Once we know the radius and height, substitute those values in the formula volume = πr²h
To find the volume, multiply the base area by the height. Volume = π x r x r x h.
Tips and Tricks for Calculating the Volume of Oblique Cylinder
Remember the formula: The formula for the volume of an oblique cylinder is simple: Volume = πr²h
Break it down: The volume is how much space fits inside the cylinder. Calculate the base area (πr²) and then multiply by the height.
Simplify the numbers: If the radius and height are simple numbers like 2, 3, or 4, it is easy to calculate. For example, for r=3 and h=4, πr²h = π × 3² × 4.
Check for π approximations: If you need to approximate π, you can use 3.14 or 22/7, depending on the level of precision required.
Common Mistakes and How to Avoid Them in Volume of Oblique Cylinder
Making mistakes while learning the volume of the oblique cylinder is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of oblique cylinders.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area involves different calculations, but volume is calculated by the base area times the height. For example, the volume is πr²h, not surface area formulas.
Mistake 2
Confusing Volume with Lateral Area
Some kids may think of the cylinder’s lateral area instead of the volume formula. Volume is the space inside the cylinder, whereas lateral area refers to the area of the side surface of the cylinder. Do not mix them up.
Mistake 3
Using the wrong Formula for right cylinders
Some kids use the concept of a right cylinder without realizing the principles are the same. The formula remains Volume = πr²h whether the cylinder is right or oblique.
Mistake 4
Confusing cubic volume with linear dimensions
Thinking of volume in terms of linear measurements. This happens when someone uses the radius or height (which are linear measurements) instead of understanding that volume relates to cubic measurements.
Mistake 5
Incorrectly calculating the height
Some students calculate the given volume without solving for the proper height. Ensure that the height used is the perpendicular distance between the bases.
Volume of Oblique Cylinder Examples
Problem 1
An oblique cylinder has a radius of 3 cm and a height of 5 cm. What is its volume?
The volume of the oblique cylinder is approximately 141.37 cm³.
Explanation
To find the volume of an oblique cylinder, use the formula: V = πr²h
Here, the radius is 3 cm, and the height is 5 cm, so: V = π × 3² × 5 ≈ 3.14 × 9 × 5 = 141.3 cm³
Problem 2
An oblique cylinder has a radius of 7 m and a height of 10 m. Find its volume.
The volume of the oblique cylinder is approximately 1,539.38 m³.
Explanation
To find the volume of an oblique cylinder, use the formula: V = πr²h
Substitute the radius (7 m) and the height (10 m): V = π × 7² × 10 ≈ 3.14 × 49 × 10 = 1,539.38 m³
Problem 3
The volume of an oblique cylinder is 150 cm³, and its radius is 2 cm. What is the height of the cylinder?
The height of the oblique cylinder is approximately 11.95 cm.
Explanation
If you know the volume of the cylinder and you need to find the height, rearrange the formula to solve for height: h = V / πr²
Substitute V = 150 cm³, r = 2 cm: h = 150 / (π × 2²) ≈ 150 / (3.14 × 4) ≈ 11.95 cm
Problem 4
An oblique cylinder has a radius of 1.5 inches and a height of 4 inches. Find its volume.
The volume of the oblique cylinder is approximately 28.27 inches³.
Explanation
Using the formula for volume: V = πr²h
Substitute the radius 1.5 inches and the height 4 inches: V = π × 1.5² × 4 ≈ 3.14 × 2.25 × 4 = 28.27 inches³
Problem 5
You have an oblique cylinder-shaped container with a radius of 5 feet and a height of 8 feet. How much space (in cubic feet) is available inside the container?
The container has a volume of approximately 628.32 cubic feet.
Explanation
Using the formula for volume: V = πr²h
Substitute the radius 5 feet and the height 8 feet: V = π × 5² × 8 ≈ 3.14 × 25 × 8 = 628.32 ft³
FAQs on Volume of Oblique Cylinder
1.Is the volume of an oblique cylinder the same as the surface area?
2.How do you find the volume if the radius and height are given?
3.What if I have the volume and need to find the height?
4.Can the radius or height be a decimal or fraction?
5.Is the volume of an oblique cylinder the same as the surface area?
Important Glossaries for Volume of Oblique Cylinder
- Radius: The distance from the center to any point on the edge of the base.
- Height: The perpendicular distance between the bases of the cylinder.
- Volume: The amount of space enclosed within a 3D object. In the case of an oblique cylinder, volume is calculated by multiplying the base area by the height.
- Cubic units: The units of measurement used for volume. If the radius is in centimeters (cm), the volume will be in cubic centimeters (cm³); if in meters, it will be in cubic meters (m³).
- Base Area: The area of the circular base, calculated as πr².
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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
