101 LearnersLast updated on July 20th, 2025
Volume of Right Circular Cone
The volume of a right circular cone is the total space it occupies or the number of cubic units it can hold. A right circular cone is a 3D shape with a circular base and a pointed top, called the apex. To find the volume of a right circular cone, we use the formula involving its base radius and height. In real life, kids relate to the volume of a right circular cone by thinking of things like an ice cream cone or a funnel. In this topic, let’s learn about the volume of the right circular cone.
What is the volume of a right circular cone?
The volume of a right circular cone is the amount of space it occupies.
It is calculated by using the formula: Volume = (1/3)πr²h Where 'r' is the radius of the base and 'h' is the height of the cone.
Volume of Right Circular Cone Formula A right circular cone is a 3-dimensional shape with a circular base and a height perpendicular to the base.
To calculate its volume, you multiply the area of the base (πr²) by the height and then divide by three.
The formula for the volume of a right circular cone is given as follows: Volume = (1/3)πr²h
How to Derive the Volume of a Right Circular Cone?
To derive the volume of a right circular cone, 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 any cone is: Volume = (1/3) × Base Area × Height
For a right circular cone: Base Area = πr² (since the base is a circle) The volume of a right circular cone will be, Volume = (1/3) × πr² × h Volume = (1/3)πr²h
How to find the volume of a right circular cone?
The volume of a right circular cone is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³).
Use the base radius and height in the formula to find the volume.
Let’s take a look at the formula for finding the volume of a right circular cone: Write down the formula Volume = (1/3)πr²h 'r' is the radius of the base, and 'h' is the height of the cone.
Once we know the radius and height, substitute those values into the formula Volume = (1/3)πr²h To find the volume, calculate the area of the base, multiply it by the height, and then divide by three.
Tips and Tricks for Calculating the Volume of Right Circular Cone
Remember the formula: The formula for the volume of a right circular cone is: Volume = (1/3)πr²h Break it down: The volume is how much space fits inside the cone.
Calculate the area of the base first, then multiply by height and divide by three.
Simplify the numbers: Use simple values for π (like 3.14) to make calculations easier.
Check for the correct radius and height: Ensure you are using the correct measurements for the base radius and the height perpendicular to the base.
Common Mistakes and How to Avoid Them in Volume of Right Circular Cone
Making mistakes while learning the volume of a right circular cone is common.
Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of cones.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area.
Surface area involves both the lateral area and the base area, while volume is calculated by using (1/3)πr²h.
For example, the volume is not the same as the surface area formula.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the cone’s perimeter (circumference of the base) instead of the volume formula.
Volume is the space inside the cone, whereas perimeter refers to the distance around the circle.
Do not mix them up.
Mistake 3
Using the wrong formula for cylinders
Some kids use the formula for the volume of a cylinder (πr²h) instead of the cone formula.
Remember, the cone volume is one-third of the cylinder with the same base and height.
Mistake 4
Confusing cubic volume with linear volume
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 base area
Some students incorrectly calculate the base area. Make sure to calculate πr² correctly before using it in the volume formula.
Volume of Right Circular Cone Examples
Problem 1
A cone has a base radius of 3 cm and a height of 4 cm. What is its volume?
The volume of the cone is 37.68 cm³.
Explanation
To find the volume of a cone, use the formula: V = (1/3)πr²h Here, r = 3 cm, h = 4 cm, so: V = (1/3)π(3)²(4) = (1/3)π(9)(4) = 37.68 cm³ (using π ≈ 3.14)
Problem 2
A cone has a base radius of 5 m and a height of 10 m. Find its volume.
The volume of the cone is 261.67 m³.
Explanation
To find the volume of a cone, use the formula: V = (1/3)πr²h Substitute r = 5 m, h = 10 m: V = (1/3)π(5)²(10) = (1/3)π(25)(10) = 261.67 m³ (using π ≈ 3.14)
Problem 3
The volume of a cone is 150 cm³. If the 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 formula: V = (1/3)πr²h 150 = (1/3)π(5)²h 150 = (1/3)π(25)h h = (150×3)/(π×25) ≈ 5.73 cm
Problem 4
A cone has a base radius of 2.5 inches and a height of 6 inches. Find its volume.
The volume of the cone is approximately 39.27 inches³.
Explanation
Using the formula for volume: V = (1/3)πr²h
Substitute r = 2.5 inches, h = 6 inches: V = (1/3)π(2.5)²(6) = (1/3)π(6.25)(6) = 39.27 inches³ (using π ≈ 3.14)
Problem 5
You have a cone-shaped container with a base radius of 3 feet and a height of 9 feet. How much space (in cubic feet) is available inside the container?
The container has a volume of approximately 84.78 cubic feet.
Explanation
Using the formula for volume: V = (1/3)πr²h Substitute r = 3 feet, h = 9 feet: V = (1/3)π(3)²(9) = (1/3)π(9)(9) = 84.78 ft³ (using π ≈ 3.14)
FAQs on Volume of Right Circular Cone
1.Is the volume of a cone the same as the surface area?
2.How do you find the volume if the base radius and height are given?
3.What if I have the volume and need to find the height?
4.Can the base radius or height be a decimal or fraction?
5.Is the volume of a cone the same as the surface area?
Important Glossaries for Volume of Right Circular Cone
- Radius: The distance from the center of the base to its circumference. It is used in calculating the base area.
- Height: The perpendicular distance from the base to the apex of the cone. It is used in calculating the volume.
- Volume: The amount of space enclosed within a 3D object. In the case of a cone, the volume is calculated using the base area and height. It is expressed in cubic units (e.g., cm³, m³).
- Base Area: The area of the circular base of the cone, calculated as πr².
- Apex: The pointed top of the cone, opposite the base.
Explore More measurement
![Important Math Links Icon]()
Previous to Volume of Right Circular Cone
![Important Math Links Icon]()
Next to Volume of Right Circular Cone
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
