Volume of Right Circular Cone
The volume of a right circular cone is the space occupied by the right circular cone or the capacity of the right circular cone. A cone is a threedimensional solid object which is having a circle at one end and a pointed end on the other. The pointed end is also known as the vertex of the cone. A right circular cone is a cone whose axis is perpendicular to the plane of the base. A right circular cone is generated by a revolving right triangle about one of its legs. In this section, we will learn about the volume of the right circular cone along with a few solved examples and practice questions.
1.  What Is the Volume of Right Circular Cone? 
2.  Volume of Right Circular Cone Formula 
3.  Calculation of Volume of Right Circular Cone 
4.  FAQs on Volume of Right Circular Cone 
What Is the Volume of Right Circular Cone?
The volume (V) of a right circular cone can be defined as the space occupied by the right circular cone. The volume of the right circular cone is equal to onethird of the product of the area of the circular base and its height.
The formula for the volume is V = (1/3) × πr^{2}h.
where r is the radius of the base circle and h is the height of the cone.
If we correlate the volume of the cylinder and the right circular cone, the volume of the right circular cone is onethird of the volume of the cylinder of the same radius and height.
The volume of the right circular cone = (1/3) × volume of a cylinder
We can see that from the image shown below.
Volume of Right Circular Cone Formula
The volume of the cone is equal to onethird of the product of the area of the base and its height. The base area of the cone is obtained by multiplying the square of its radius to π. Thus, the formula for the volume of the right circular cone, with a radius r and height h is "(1/3)πr^{2}h".
Calculation of Volume of Right Circular Cone
The volume of the right circular cone is equal to (1/3)πr^{2}h". By following the steps mentioned below we can find the volume of a right circular cone.
 Step 1: Calculate the radius of the base of the cone and height of the cone.
 Step 2: Find the square of the radius.
 Step 3: Find out the product of the square of its radius to π. This will give the area of the circular base of the cone.
 Step 4: Multiply the result with the height of the cone.
 Step 5: Multiply the result thus obtained with 1/3.
 Step 6: Represent the answer in cubic units.
Solved Examples on Volume of Right Circular Cone

Example 1
The radius of a right circular cone is 5 in. Find the volume of the right circular cone if the height is 15 in.
Solution
Length of the radius, r = 5 in
Height of the cone, h = 15 in
Using the formula for the volume of the right circular cone,
V = (1/3)πr^{2}h
V = (1/3) π × 5^{2 }× 15
V = π × 5^{2 }× 5
V = 392.7
Therefore, the volume of the right circular cone is 392.6 cubic inches.

Example 2
Emanuel has given the volume of the right circular cone as 244π cubic units. Find the radius of the circular base of the cone if the height of the cone is 183 units.
Solution
The volume of the right circular cone, V = 244π
Height of the cone, h = 183
Using the formula for the volume of the right circular cone,
V = (1/3)πr^{2}h
244π = (1/3) π × r^{2}× 183
4 = r^{2}
r = 2
So, the radius of the cone is 2 units.
FAQs on Volume of Right Circular Cone
What Is a Right Circular Cone?
A right circular cone is the one whose axis is perpendicular to the plane of the base. A right circular cone is generated by revolving a right triangle about one of its legs.
What Is the Volume of a Right Circular Cone?
Volume of a Cone = (1/3)πr^{2}h, where r is the radius and h is the height of the cone.
What Is the Surface Area or Total Surface Area of a Right Circular Cone?
Total Surface Area of a Cone = πr^{2 }+ πrs
Total Surface Area of a Cone = πr^{2}+πr√(r^{2}+h^{2})
where r is the radius, s is the slant height, and h is the height of the cone.
What Is the Curved Surface Area of a Right Circular Cone?
Curved Surface Area of a Cone = πrs = πr√(r^{2}+h^{2})
where r is the radius, s is the slant height, and h is the height of the cone.
How Can You Find the Radius of a Cone?
The radius of a cone refers to the radius of its circular base.
The radius of a cone could be found using its volume and height.
How Many Vertices Are There in a Right Circular Cone?
There is only one vertex in a right circular cone.
Does a Cone Have Two Faces?
A cone has only one circular face.
How Do You Find the Side Length/ Slant Height of a Right Cone?
The height of the cone, the slant height, and the radius of the base form a right triangle. So, we can use the Pythagorean theorem to find the slant height.
Is It Possible To Find the Right Circular Cone With the Same Height and Slant Height?
A right circular cone cannot have the same height as its slant height. If the slant height is considered as the hypotenuse of the right triangle, then we know that the length of the hypotenuse is greater than the lengths of the remaining two sides of the triangle.