Volume of Cone
2026-02-28 00:56 Diff
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Last updated on November 27, 2025

A cone is a three-dimensional shape with a circular base and a single pointed tip called the vertex. Some common examples include traffic cones and party hats. A cone is formed by rotating a right-angled triangle around one of its sides. The volume of a cone refers to the amount of space it takes up. In this topic, we will explore how to calculate the volume of a cone.

What is the Volume of a Cone?

The volume of a cone is measured in cubic units such as cm3, m3, in3, etc

The cone’s structure includes both a curved surface area and a flat circular base. The base is connected to the vertex by every point on it’s surface area.

The volume of a cone is calculated using its radius and height. 

Volume of Cone Formula

The volume of a cone is the product of one-third of the area of its base and its vertical height. Mathematically, the formula is written as V = 13r2h cubic units.

Here, r is the radius of the base, h is the perpendicular height from the base to the vertex, and the value of =3.14 or 22/7.

If the diameter of the cone is given but not the radius, the radius of the cone can be found by dividing the diameter by 2. 


The volume of cone can also be found using formula V=1/12 πd2h. 


This formula is found by substituting the valure of r with d/2:


V = 1/3πr2h   


Substituting r = d/2


V = 1/3π(d/2)2h 


V = 1/3(d2/4)h


V =1/12 π d2h 

In case the height of the cone is not given, but the slant height is, we can find the height using Pythagorean theorem i.e., h=√l2-r2

Here, h is the height of the cone


l is the slant height, and 


r is the radius

How to Derive the Volume of Cone Formula?

To derive the formula for the volume of a cone, we start by considering a cylinder with the same height (h) and radius (r) as the cone. The height and radius are essential because the volume of a cone depends on the area of its circular base (which uses the radius) and how tall the cone is (its height), both of which directly affect the space it occupies

When we try to fill the cylinder using the cone, we find that a total of 3 cones are required to fill one cylinder.

Since we already know the volume of a cylinder = πr2h, and we have established that the volume of a cone having the same radius is one-third the volume of a cylinder.

So, Volume of cone =1/3πr2h.

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How to Find the Volume of Cone?

The volume of a cone can be found by substituting the values of the required parameters given in the formula. 

  • Make a note of all known parameters: the radius ‘r’, diameter ‘d’, slant height ‘l’ and height ‘h’. 
  • Apply one of the two formulas depending on the given parameters:

Volume of cone using radius: V=1/3πr2h or V=1/3π r2  √l2-r2

Volume of cone using diameter: V=1/12πd2h

  • Write the final answer in a cubic unit.

Tips and Tricks for Calculating the Volume of Cone

Understanding the volume of a cone becomes easier with the help of some useful tips. These tricks can help students avoid confusion, remember key steps, and solve problems more efficiently.

  • Always make sure that units are uniform throughout, i.e., check that the radius and height are of the same unit.
  • Volume should always be in cubic units.
  • Use =22/7 when the radius is divisible by 7, and use =3.14 for other values of the radius. This makes calculations easier.
  • Draw and label the diagram of a cone for visual help while solving for its volume.
  • Follow the process step by step to avoid missing steps like squaring.
     

Common Mistakes and How to Avoid Them in Volume of Cone Calculations

When calculating the volume of a cone, along with the formula, it is necessary to pay attention the given values and unit conversion. Here are a few common mistakes to avoid:

Problem 1

A cone has a radius of 3 cm and a height of 4 cm. Find its volume.

Okay, lets begin

37.68 cm3
 

Explanation

Volume of a cone = 1/3 πr2h


=1/3 x 3.14 x 32 x4

=1/ 3 x 3.14x 9 x 4


=1/3 x 113.04

=37.68 cm3

Well explained 👍

Problem 2

A cone has a diameter of 10cm and a height of 12 cm. Find its volume

Okay, lets begin

 314cm3
 

Explanation

Radius r=10/2 = 5cm


Volume = 1/3 πr2h

=1/3 x 3.14 x 52 x 12


=1/ 3 x 3.14 x 25 x 12


= 1/3 x 942

=314 cm3
 

Well explained 👍

Problem 3

A cone has a radius of 2.5 cm and a height of 6 cm. Find the volume.

Okay, lets begin

39.25 cm3 
 

Explanation

 Volume = 1/3 πr2h


=1/3 x 3.14 x (2.5)2 x 6


= 1/3 x 3.14 x 6.25 x 6


=1/3 x 117.75

=39.25 cm3

Well explained 👍

Problem 4

Find the volume of a cone with radius 7 cm and height 15 cm. Use =22/7

Okay, lets begin

770 cm3
 

Explanation

Volume = 1/3 πr2h


=1/3 x 22/7 x 72 x 15


= 1/3 x 22/7 x 49 x 15


=1/ 3 x 16170/7


= 16170/21

= 770 cm3

Well explained 👍

Problem 5

A birthday party hat is shaped like a cone with a base radius of 6 cm and a height of 10 cm. What is its volume?

Okay, lets begin

376.8 cm3
 

Explanation

Volume = 1/3 πr2h


= 1/3 x 3.14 x 62 x 10


=1/3 x 3.14 x 36 x 10


= 1/3 x 1130.4

=376.8 cm3

Well explained 👍

FAQs on Volume of Cone

1. What is a cone?

  A Cone is a 3-D geometric shape with a flat circular base and apex or vertex.
 

2.What is the formula for the volume of a cone?

 The formula for the volume of a cone is V = 1/3 πr2h. Here, r is the radius of the cone and h is its vertical height.

3.What units are used for the volume of a cone?

 The volume of a cone can be represented in cubic centimeters (cm3) or cubic meters (m3). It depends upon the units in which its radius and height is measured.
 

4. How do you find the height of a cone if you know its radius and volume?

The height of the cone can be found using the volume formula.


 V= 1/3πr2h, multiply both sides by 3:


3V = πr2h, h = 3V/ πr2, r is the radius of the cone and h is its vertical height.

5. What is the difference between the height and the slant height of a cone?

Important Glossaries for Volume of Cone

  • Vertex: A vertex is the tip or apex of the cone that is opposite to its base.
  • Curved Surface Area: It is the area covered by the curved surface of a cone, it does not include the base of a cone since the base is a flat surface.
  • Radius: It is the distance from the center of the base of a cone to its edge.
     

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.