Volume of Right Circular Cone

The volume of a right circular cone, also known as its capacity, is the space that it takes up. A right circular cone is a solid shape in three dimensions that has a circular base and a tip called the vertex. The axis, that joins the tip of the cone to the center of the base, is perpendicular to the base and is called its height. The line along which the cone can be cut in the slant height is called its slanting height. All these dimensions are required to find the volume of a right circular cone. Let’s learn more about the volume of a right circular cone in detail.

Table of Contents

• What is the Volume of a Right Circular Cone
• Formula for Volume of a Right Circular Cone
• Solved Examples on Volume of a Right Circular Cone

What is the Volume of a Right Circular Cone

The volume (V) of a right circular cone represents the amount of space that it takes up. It is equal to one-third of the area of the base circle times its height. To find the volume, we can use a simple formula V = (1/3) × πr2h, where r is the radius of the base circle and h is the height of the cone.

Formula for Volume of a Right Circular Cone

The volume of a cone is calculated as one-third of the product of its base area and height. The base area is found by squaring the radius and multiplying by π. Therefore, the formula for the volume of a right circular cone with radius r and height h is V = (1/3)πr²h.

Solved Examples on Volume of a Right Circular Cone

Example 1: The height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone.

Solution: From l2=r2+h2, we have r =  l2−r2 =  282+212 =  77 
So, volume of the cone = 1/3π r2h = 1/3 x 22/7 x 77 x  77 x 21  cm3 = 7546 cm3 

Example 2: Find the volume of a right circular cone with radius as 2 cm and height as 5 cm.

Solution: We know that, volume of the cone = 1/3π r2h
Volume of cone = 1/3 x 22/7 x 2 x 2 x 5 = 20.95cm3