In geometry, a cylinder is one of the most common three-dimensional shapes, with two parallel circular bases separated by a space. A curved surface connects the two circular bases at a fixed distance from the middle. The axis of the cylinder is a line segment that connects the centers of two circular bases. The height of the cylinder is the area covered between the two circular bases. One of the most common types of refueling equipment is the LPG gas cylinder. In this blog, we are going to explore the cylinder, surface area and volume of cylinder.
Definition of Cylinder
A cylinder is a three-dimensional solid in mathematics that holds two parallel bases at a fixed distance, connected by a curved surface. These bases are usually circular (like a circle), and a line segment called the axis connects the two bases’ centers. The height, “h,” is known as the perpendicular distance between the bases, and the distance from the axis to the outer surface is the radius “r” of the respective cylinder.
Properties of the Cylinder:
Each shape in geometry has some characteristics that differentiate one shape from another. Therefore, cylinders also have their unique characteristics that are given below:
- The bases are invariably congruent and parallel to each other.
- If the axis of the cylinder makes a right angle with the bases of the same that are exactly over each other, then it is named a “Right Cylinder”.
- It is very similar to the prism as it has the same cross-section property everywhere.
- If the bases are not precisely over each other but sideways, and the axis does not make a right angle to the bases, then it is named an “Oblique Cylinder”.
- If the bases are circular, then it is named a right circular cylinder.
- If the bases are in an elliptical shape, then it is named as an “Elliptical Cylinder”.
The cylinder has three essential quantities, based on which we have expressed the formulas.
- Lateral Surface Area or curved surface area
- Total Surface Area
Surface Area of a Cylinder:
The area covered by a cylinder’s surface in three-dimensional space is called its surface area. A three-dimensional structure with circular bases that are parallel to each other is known as a cylinder. There are no vertices in it. The surface area of three-dimensional shapes is generally referred to as the area of three-dimensional shapes. The area of the surface is measured in square units. For instance, cm², m², and so forth.
Cylinder’s Curved Surface Area
The space between the two parallel circular bases where the curved surface of the cylinder is contained. A lateral surface area is another term for it. It can be calculated using the following formula:
Curved Surface Area = 2πrh square units
Total Surface Area of Cylinder
The total surface area of a cylinder is the total sum of curved surface area and the area of two circular bases in the cylindrical shape.
TSA can be expressed as Curved surface + Area of Circular bases
TSA = 2πrh + 2πr²
We can derive from the above expression that 2πr is common. Hence,
Total surface area, A = 2πr (r + h) square units
Volume of the Cylinder
Any solid or three-dimensional form has a volume that takes up space. The cylinder’s volume is the amount of space it takes up in every three-dimensional plane. The volume of a cylinder describes the amount of water that can be immersed in it. The volume of a cylinder is obtained with the aid of the formula:
Volume (V) = πr²h cubic units
Where ‘h’ is the expressed height and ‘r’ is the radius. The volume of the cylinder and other units of measurement are all interrelated. The cylinder is a very complex shape, but with constant and persistent practice the students can understand the properties and the compositions of the cylindrical shape.