Volume of Oblique Cylinder
2026-02-28 08:25 Diff
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Last updated on September 5, 2025

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.

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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.

Problem 1

An oblique cylinder has a radius of 3 cm and a height of 5 cm. What is its volume?

Okay, lets begin

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

Well explained 👍

Problem 2

An oblique cylinder has a radius of 7 m and a height of 10 m. Find its volume.

Okay, lets begin

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

Well explained 👍

Problem 3

The volume of an oblique cylinder is 150 cm³, and its radius is 2 cm. What is the height of the cylinder?

Okay, lets begin

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

Well explained 👍

Problem 4

An oblique cylinder has a radius of 1.5 inches and a height of 4 inches. Find its volume.

Okay, lets begin

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

Well explained 👍

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?

Okay, lets begin

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

Well explained 👍

FAQs on Volume of Oblique Cylinder

1.Is the volume of an oblique cylinder the same as the surface area?

No, the volume and surface area of an oblique cylinder are different concepts: Volume refers to the space inside the cylinder and is given by V = πr²h. Surface area involves calculating the area of the curved surface and the bases.

2.How do you find the volume if the radius and height are given?

To calculate the volume when the radius and height are provided, use the formula V = πr²h. For example, if the radius is 4 cm and height is 6 cm, the volume would be: V = π × 4² × 6 = 301.44 cm³ (using π ≈ 3.14).

3.What if I have the volume and need to find the height?

If the volume of the oblique cylinder is given and you need to find the height, rearrange the formula to solve for height: h = V / πr².

4.Can the radius or height be a decimal or fraction?

Yes, the radius or height of an oblique cylinder can be a decimal or fraction. For example, if the radius is 2.5 inches and the height is 3.5 inches, the volume would be: V = π × 2.5² × 3.5 ≈ 68.66 inches³.

5.Is the volume of an oblique cylinder the same as the surface area?

No, the volume and surface area of an oblique cylinder are different concepts: volume refers to the space inside the cylinder and is given by V = πr²h.

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