A cone is a geometrical object which can be considered as a three-dimensional figure with circular and flat bases. It also consists of a sharp point known as the vertex. This is also the highest point of a cone. A cone does not consist of any edges. the volume of the cone can be defined as the total amount of cubic units that can be filled inside the cone. The volume of a cone formula is 1/3 * π * r.r * h where ‘r’ denotes the radius of the cone and ‘h’ denotes the height of the cone.
The Volume of Cylinder Formula
Volume can be defined as the scalar quantity which signifies the amount of space filled inside it. Similarly, the volume of a cylinder is regarded as the maximum amount of cubic units that can be filled inside a cylinder. A cylinder can be defined as a three-dimensional figure with two congruent and parallel bases. A cylinder is categorized into three types. Such as the right circular cylinder, oblique cylinder, and elliptic cylinder. We may solve some related examples in the coming sections of this article.
Some Examples Related to the Volume of Cone
To recall, the mathematical formula to calculate the volume of a cone is 1/3 * π * r.r * h where ‘r’ denotes the radius of the cone and ‘h’ denotes the height of the cone. Some of the examples related to the volume of a cone are mentioned below:
Example 1: Find the volume of the cone, if the height and radius of the cone are 4 cm and 8 cm respectively.
Given that,
Height of the cone = 4 cm
The radius of the cone = 8 cm
Using the formula of the volume of cone = 1/3 * π * r.r * h
1/3 * 3.14 * 8 * 8 * 4 = 1/3 * 3.14 * 256
1/3 * 3.14 * 256 = 1/3 * 803.84
1/3 * 803.84 = 241.152 cm cubic units.
Hence, the volume of the cone = 241.152 cm cubic units.
Example 2: Calculate the volume of the cone, if the height and radius of the cone are 12 cm and 16 cm respectively.
Given that,
Height of the cone = 12 cm
The radius of the cone = 16 cm
Using the formula of the volume of cone = 1/3 * π * r.r * h
1/3 * 3.14 * 16 * 16 * 12 = 1/3 * 3.14 * 3072
1/3 * 3.14 * 3072 = 1/3 * 9646
1/3 * 9646 = 2893,824 cm cubic units.
Thus, the volume of the cone = 2893.824 cm cubic units.
Some Examples Related to the Volume of Cylinder
As mentioned above, the volume of a cylinder formula is πr.r.h, where ‘r’ denotes the radius of the cone and ‘h’ denotes the height of the cone. Some of the examples are mentioned below.
Example 1: Find the volume of the Cylinder if the height and radius of the cylinder are 6 cm and 4 cm respectively, the value of π to be taken as 3.14?
Given that,
Radius of the cylinder = 4 cm
Height of the cylinder = 6 cm
Using the formula for the volume of the cylinder: πr.r.h.
3.14 * 4 * 4 * 6 = 3.14 * 96
3.14 * 96 = 301.44 cm cubic units.
Thus, the volume of the cylinder for the given height and radius is = 301.44 cm cubic units.
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