Volume of a Cone

A cone is a three-dimensional geometric shape having a circular base that tapers from a flat base to a point called apex or vertex. Here we will learn how to find out the volume of a cone. A cone is formed by a set of line segments, half-lines or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex. A cone can be seen as a set of non-congruent circular disks that are stacked on one another such that ratio of the radius of adjacent disks remains constant.

How to Find the Volume of a Cone?

You can think of a cone as a triangle which is being rotated about one of its vertices. Now, think of a scenario where we need to calculate the amount of water that can be accommodated in a conical flask. In other words, we mean to calculate the capacity of this flask. The capacity of a conical flask is basically equal to the volume of the cone involved. Thus, the volume of a three-dimensional shape is equal to the amount of space occupied by that shape. Let us perform an activity to calculate the volume of a cone.

volume of a cone

Take a cylindrical container and a conical flask of the same height and same base radius. Add water to the conical flask such that it is filled to the brim. Start adding this water to the cylindrical container you took. You will notice it doesn’t fill up the container fully. Try repeating this experiment for once more, you will still observe some vacant space in the container. Repeat this experiment once again; you will notice this time the cylindrical container is completely filled. Thus, the volume of a cone is equal to one-third of the volume of a cylinder having the same base radius and height.

Volume of a Cone Formula

In general, a cone is a pyramid with a circular cross-section. A right cone is a cone with its vertex above the surface. When it is not mentioned as a ‘cone’ is referred to as a ‘right-cone’. You can easily find out the volume of a cone if you have the measurements of its height and radius and put it into a formula.

volume of a cone formula

Therefore, the volume of a cone formula is given as

The volume of a cone = (1/3) πr2h cubic units

Where,

‘r’ is the base radius of the cone

‘l’ is the slant height of a cone

‘h’ is the height  of the cone

Volume of a Cone Example

Example: Calculate the volume if r= 2 cm and h= 5 cm.

Solution:

Given:

r = 2

h= 5

Using the Volume of Cone formula

The volume of a cone = (1/3) πr2h cubic units

V= (1/3) × 3.14 × 2×5

V= (1/3) × 3.14 × 4 ×5

V= (1/3) × 3.14 × 20

V = 20.93 cm3

Therefore, the volume of a cone = 20.93 cubic units.

 

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