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Mensuration is very important and very applicable in our everyday life. We often have to measure the areas. You would have heard the term lateral surface areas, but let’s know what it is, giving special reference and importance to the curved surface area of the cylinder. 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 curved surface area and total surface area.
Areas of 3-D figures
Generally, the area of 3D figures is measured in the following two ways :
- Total Surface Area
- Curved Surface Area
Total surface area is the space filled by a three-dimensional object’s external surface. 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 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.
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 right circular 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.
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.
Curved Surface Area of a Cylinder
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.
We know that the curved surface of the cylinder is a rolled-up rectangle, so its area will be length multiplied by breadth.
The length of the cylinder = the circumference of the base = 2πr.
The rectangle’s width = the cylindrical can’s height = h.
We know that the rectangle Equals the area of the curved surface of the Cylindrical Can = lb = 2πrh.
The Formula for Curved Surface Area of Cylinder = 2rh
Conclusion
We hope that now you would have understood the curved surface of a cylinder, how to get it, and where we get the formula of the curved surface of the cylinder. You can attempt some questions and exercises to check your understanding and application of the concept. This concept is not just helpful in terms of competitive exams or studies but is also very applicable to daily life and real problems.
