Volume of Cylinder

A cylinder is a three-dimensional solid consisting of two parallel circular bases joined together by a curved surface at a particular distance from the center of the circular bases.

Properties of Cylinder

1. It has 1 curved surface and 2 circular faces.
2. It has 2 curved edges and zero vertices.
3. It has 2 identical, circular bases which are parallel and congruent.

Types of Cylinder

In geometry, there are 4 types of cylinders:

1. Right circular cylinder: A cylinder whose axis is perpendicular to both bases.

2. Oblique cylinder: A cylinder whose axis is not perpendicular to both bases.

3. Elliptic cylinder: A cylinder whose bases are in the form of an ellipse.

4. Hollow cylinder: A cylinder in which two circular cylinders are bound one inside the other.

Volume of a Right Circular Cylinder

The volume of a right circular cylinder is the amount of space inside the cylinder.

Formula for Volume of a Right Circular Cylinder

V = πr²h

where:
V is the volume
π (pi) is a mathematical constant (approximately 3.14)
r is the radius of the cylinder (half of the diameter)
h is the height of the cylinder

Formula for Volume of a Hollow Cylinder

V = π (R² - r²)h

where:
R is the outer radius of the cylinder
r is the inner radius of the cylinder
h is the height of the cylinder
π (pi) is a mathematical constant (approximately 3.14)

Unit of Volume

The volume of a cylinder is usually measured in cubic units, such as cubic centimetres (cm³), cubic metres (m³), cubic feet (ft³) and so on. It can be also measured in litres or kilolitres.

Relationship between Litre and Cubic Metre and Litre and Centimetre

1 m³ = 1000 L
1 L = 1000 cm³