Volume of Cone

A cone is a geometrical shape that can be defined as a three-dimensional shape with circular bases. Based on the bases, a cone is further classified into various types. Some of them are the right circular cone, oblique cone, and many others. Mathematically, a cone can be formed when a triangle rotates around the vertices of it. For a right circular cone, the vertex is found above the center of the base whereas, in an oblique cone, the vertex is not found above the right circular cone. Now,the volume of a cone is the total cubic units filled inside a cone Or the total amount of cubic units which a cone can hold. The mathematical formula to find the volume of the cone is (1/3)πr.r.h where ‘r’ is the radius of the cone and ‘h’ is the height of the cone. You must note that the resultant value for the volume of a cone is always written in cubic units. For instance, cm cubic units or meter cubic units. In this article, we shall cover some interesting topics related to the volume of different geometrical figures. Such as the volume of cuboid, examples related to it, and so on.

Volume of a Cuboid

A cuboid is a geometrical figure which is considered a three-dimensional shape with 8 vertices, 12 edges, and 6 faces. A three-dimensional shape has three dimensions, they are length, width, and height. You must not confuse yourself that a cuboid is a cube. More often than not, a cuboid is considered a cube because both of them resemble similar properties. Now, the volume of a cuboid is the total amount of space that a cuboid can hold inside it or the measure of the total area occupied inside a cuboid. The mathematical formula to find the volume of a cuboid is l * b * h where ‘l’ is the length of the cuboid and ‘b’ is the breadth and ‘h’ is the height of the cuboid. Thus, the product of length, breadth, and height is the volume of the cuboid. Here, the resultant value is also written similar to that of the volume of a cube i.e. cubic units. We shall solve some examples based on them in the coming sections.

Examples 

As mentioned, the mathematical formula to find the volume of a cuboid is l * b * h where ‘l’ is the length of the cuboid and ‘b’ is the breadth and ‘h’ is the height of the cuboid. Some examples based on it are given below.

Example 1: Find the volume of cuboid if the measure of length, breadth, and height is 3, 4, and 5 cm respectively.

Solution:

              Given that,

              Length of cuboid = 3 cm

               Breadth of cuboid = 4 cm

               Height of cuboid = 5 cm

               Using the formula, l * b * h

               3 * 4 * 5 = 60 cm cubic units.

               Hence, the volume of cuboids is 60 cm cubic units.

Examples of Volume of Cube

To recall, the mathematical formula to find the volume of a cone is (1/3)πr.r.h where ‘r’ is the radius of the cone and ‘h’ is the height of the cone. Some examples are:

Example 1: Find the volume of the cube if the radius and height of the cube are 6 cm and 8 cm respectively?

Solution:

                  Given that,

                  Height of cube = 8 cm.

                  Radius of Cube = 6 cm.

                  Using the formula = (1/3)πr.r.h

1/3 * 3.14 * 6 * 6 * 8 = 1/3 * 3.14 * 36 * 8

                  1/3 * 3.14 * 36 * 8 = 1/3 * 902.32

                   1/3 * 902.32 = 1193.74 cm cubic units.

                    Hence, the volume of the cube for the measure of radius and height is 1193.74 cubic units.

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