110 LearnersLast updated on July 9th, 2025
Volume of Oblique Cone
The volume of an oblique cone is the total space it occupies or the number of cubic units it can hold. An oblique cone is a 3D shape where the apex is not aligned directly above the center of its base. To find the volume of an oblique cone, we use the formula involving the base area and the height. In real life, kids can relate to the volume of an oblique cone by thinking of things like a tilted ice cream cone or a party hat. In this topic, let’s learn about the volume of an oblique cone.
What is the volume of the oblique cone?
The volume of an oblique cone is the amount of space it occupies. It is calculated by using the formula: Volume = (1/3) × π × r² × h Where ‘r’ is the radius of the base and ‘h’ is the perpendicular height from the base to the apex.
Volume of Oblique Cone Formula An oblique cone has a circular base and slant height but its apex is not directly above the center of the base.
To calculate its volume, you use the perpendicular height (h) and the radius (r) of the base. The formula for the volume of an oblique cone is given as follows: Volume = (1/3) × π × r² × h
How to Derive the Volume of an Oblique Cone?
To derive the volume of an oblique cone, we use the concept of volume as the total space occupied by a 3D object.
Although the cone is oblique, the formula remains the same as that of a right cone: Volume = (1/3) × Base Area × Height For a cone with a circular base: Base Area = π × r²
Thus, the volume of an oblique cone will be, Volume = (1/3) × π × r² × h
How to find the volume of an oblique cone?
The volume of an oblique cone is always expressed in cubic units, for example, cubic centimeters (cm³) or cubic meters (m³). To find the volume, use the radius of the base and the perpendicular height.
Let’s take a look at the formula for finding the volume of an oblique cone: Write down the formula Volume = (1/3) × π × r² × h The radius is the distance from the center of the base circle to its perimeter.
Once we know the radius and the perpendicular height, substitute these values into the formula to find the volume.
Tips and Tricks for Calculating the Volume of Oblique Cone
Remember the formula: The formula for the volume of an oblique cone is simple: Volume = (1/3) × π × r² × h
Break it down: The volume is how much space fits inside the cone. Use the perpendicular height and radius for your calculations. Simplify the numbers: Use 3.14 for π to make calculations easier if an exact value is not required.
Check for correct measurements: Ensure you use the perpendicular height, not the slant height, in your calculations.
Common Mistakes and How to Avoid Them in Volume of Oblique Cone
Making mistakes while learning the volume of the oblique cone is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of oblique cones.
Mistake 1
Confusing Perpendicular Height with Slant Height
Some students confuse the perpendicular height with the slant height. The perpendicular height is used in the volume formula, not the slant height.
Mistake 2
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area involves the lateral surface and base area, while volume is calculated by (1/3) × π × r² × h.
Mistake 3
Using the wrong Formula for Cylinders
Some students use the formula for the volume of a cylinder (π × r² × h) instead of the cone formula.
Mistake 4
Incorrect use of π
Some students use incorrect values for π. It’s important to use 3.14 or 22/7 when an approximation is needed.
Mistake 5
Incorrectly calculating the radius or height
Some students incorrectly identify the radius or height, leading to errors in their calculations. Ensure you understand the cone's dimensions properly.
Volume of Oblique Cone Examples
Problem 1
An oblique cone has a base radius of 3 cm and a perpendicular height of 5 cm. What is its volume?
The volume of the oblique cone is 47.1 cm³.
Explanation
To find the volume of an oblique cone, use the formula: V = (1/3) × π × r² × h
Here, the radius (r) is 3 cm, and the height (h) is 5 cm, so: V = (1/3) × π × 3² × 5 ≈ 47.1 cm³
Problem 2
An oblique cone has a base radius of 6 m and a height of 10 m. Find its volume.
The volume of the oblique cone is 376.8 m³.
Explanation
To find the volume of an oblique cone, use the formula: V = (1/3) × π × r² × h
Substitute the radius (6 m) and height (10 m): V = (1/3) × π × 6² × 10 ≈ 376.8 m³
Problem 3
The volume of an oblique cone is 150 cm³, and its base radius is 5 cm. What is the height of the cone?
The height of the cone is approximately 5.73 cm.
Explanation
If you know the volume of the cone and need to find the height, rearrange the volume formula: V = (1/3) × π × r² × h h = V / ((1/3) × π × r²)
Substitute V = 150 cm³ and r = 5 cm: h ≈ 5.73 cm
Problem 4
An oblique cone has a base radius of 4 inches and a height of 7 inches. Find its volume.
The volume of the oblique cone is approximately 117.3 inches³.
Explanation
Using the formula for volume: V = (1/3) × π × r² × h
Substitute the radius (4 inches) and height (7 inches): V = (1/3) × π × 4² × 7 ≈ 117.3 inches³
Problem 5
You have an oblique cone with a base radius of 2 feet and a height of 8 feet. How much space (in cubic feet) is available inside the cone?
The cone has a volume of approximately 33.5 cubic feet.
Explanation
Using the formula for volume: V = (1/3) × π × r² × h Substitute the radius (2 feet) and height (8 feet): V = (1/3) × π × 2² × 8 ≈ 33.5 ft³
FAQs on Volume of Oblique Cone
1.Is the volume of an oblique cone 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 cone the same as the surface area?
Important Glossaries for Volume of Oblique Cone
- Radius: The distance from the center of the base circle to its perimeter.
- Height: The perpendicular distance from the base to the apex of the cone.
- Volume: The amount of space enclosed within a 3D object. For an oblique cone, it is calculated using (1/3) × π × r² × h.
- 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 of the cone, calculated as π × r².
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
