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Mensuration and mapping are favourite topics of competitive exams to ask questions from, and one of the mathematical topics directly related to ordinary and daily life. In this article, you will learn about the cylinder, its properties, and total surface area with special reference to the right circular cylinder. After reading this article, you will be enlightened about how the cylinder’s total surface area is calculated and its formula. This will help you solve the numerical problems related to this concept. So do read till the last to master the relevant and important topic.
Areas Of 3D figures
When we consider two-dimensional figures, we have to look at and calculate the total area. Here the area is the space occupied by the figure. But in the case of three-dimensional figures or surfaces, we have two different types of area. Here we have two areas: curved surface area and total surface area.
Total surface area is the space filled by a three-dimensional object’s external surface. The total surface area of an object is the total area or the space occupied by the object irrespective of the curve or flat. It is the sum of curved surface area and area of bases.
Curved Surface Area /Lateral Surface Area is a part of this total surface area, but we can calculate it separately, which is widely applicable in many problems. The area of merely the curved component of a surface is called the curved surface area of the figure, keeping in mind that the bases are excluded. If we take the example of the cylinder, the area of the curved column, which is a rolled-up rectangle, is the curved surface area of the cylinder.
Cylinder
A cylinder is the most widely seen geometric 3D shape. We all have seen cylinders in many of our everyday objects, such as fuel containers, toilet paper, and coffee mugs. This shape-cylinder comes from the word ‘kulindros.’ The word ‘kulindros’ means tumbler, a utensil in a cylindrical shape.
A cylinder is a closed solid object with two parallel bases that are often round in shape and two parallel sides that join them. A curved column with circular bases can also be characterised as a cylinder. The cylinder is made up of two circles and one rectangle.
The bases or the circular disk are always congruent and parallel if we talk about the right circular cylinder. This means the radius is always fixed and the same for both the disks.
If we look at the structure of the cylinder, we get two disks and a rectangle if we unroll the cylinder. The cylinder’s axis is the line that runs through the centre of the two circular bases.
Height (h) is the perpendicular distance between the two bases, as shown in the diagram. A radius is assigned to each base. The radius of the cylinder, denoted by “r,” is the distance between the centre and the outer limit of the two circular bases.
The cylinder’s surface area and volume can be calculated using the height and radius measurements.
Total Surface Area Of Cylinder
As we already know, a cylindrical form comprises two circular bases and a rectangle-like shape that connects the two bases. As a result, the area of the two bases and the curved surface area must be included in the overall surface area of this geometrical form. As a result, total surface area of the cylinder = Area of base 1 + Area of base 2 + Curved surface area = πr^2 +πr^2 + 2πrh = 2πr (r+h).
As a result, the Surface Area of a Cylinder is equal to 2πr (r+h).
Cylinder Properties
Every geometrical form has unique qualities or properties that set it apart. Let’s look at some of the qualities of a cylinder form, which are given below:
- A cylinder has one curved surface and two identical flat sides.
- The two circular bases are identical in size.
- The radius of the base and the height of the curved surface determine its size.
- Unlike a cone, cube, or cuboid, a cylinder has no vertex. It denotes that the cylinder lacks a certain corner.
- The cylinder’s base and top are identical, i.e., it has the same round or elliptical base.
Conclusion
We hope that you must have understood the concept related to the total surface area of the cylinder. You can apply this concept and the formula of the surface area of the cylinder to solve many numerical problems asked in examinations and the problems related to this that we encounter in our daily lives.
