Cylinder-Total Surface Area

The cylinder is a geometrical shape and it is three dimensional. Any shape has a specific perimeter, area, etc. and to calculate such things, formulas are required specifically. This document will consist of valuable data regarding the total surface area of a cylinder. There are two types of area, the other one except the total surface area is lateral surface area. However, this document will include an analysis of the formula of the total surface area of a cylinder only. 

Total surface area of a cylinder

What is a cylinder?

The word ‘cylinder’ may depict a lot of meanings in different senses, however, as per the language of mathematics, a cylinder is a geometrical shape. It consists of two parallel bases that are connected by a curved surface. It is three dimensional and the distance between parallel bases is fixed. The bases signify circle shapes and their centres are linked with the help of a line segment that is known as an axis. For example, a candle, electrical fuse or a pipe is a cylinder and these have all the characteristics mentioned above. 

Introduction to cylinder area

The cylinder area refers to the overall region that is coerced by a cylinder-shaped object in three-dimensional space. The cylinder area is measured by summing up the measurements of the area of two bases and the curved area. The cylinders that have the circular bases placed in a complete parallel position are called right cylinders and the axis line between them forms a right angle in respect to the base. The cylinders that do not have circular bases in parallel cannot form axis lines. The various parameters that are required to calculate the area of a cylinder are height, base, side, axis and radius.

Concept of the surface area of a cylinder

Surface area refers to the area that is occupied by a cylinder from three-dimensional space. The three-dimensional shapes from the surface area and circular bases play the main role in this context as cylinders do not have vertices. The surface area is measured with square units such as m2, cm2. To calculate the surface area of a cylinder the area of circular bases and area of curved surface are added together. 

Formula

“Surface area of a cylinder = Curved surface + Area of circular bases  

Or, 2πr (h + r) square units, where, pi (π) = 22/7 or 3.142.”

Here, r refers to the radius of the cylinder and h refers to the height of the cylinder. 

The total surface area of a cylinder 

A cylinder has two types of surface areas such as total surface area and lateral or curved surface area. This study is centred on total surface area and to calculate the total surface area of a cylinder it is necessary, to sum up, the areas of all the faces of a cylinder. A cylinder that has a height of h unit and the radius is r unit will have a total surface area of the following unit, 

TSA (short form of total surface area) = 2πr (h + r) square units. 

Formula 

The formula to calculate TSA of a cylinder is given below,

TSA = 2π * r * h + 2πr2 = 2πr (h + r) square units.

Surface area deviation of a cylinder

It is important to provide realistic scenarios to support the mathematical formulas. Suppose it is necessary, at a moment, to paint the circular faces of a cylindrical structure. It is important to find out the amount of paint that will be required to paint every wall. For this reason, the area of every face must be calculated and this calculation of all the faces refers to the total surface area of a cylinder or cylindrical structure. 

The cylindrical structure has a height of h units and a radius of r units. The curved surface is signified as the diameter (d = 2r) of a circular base and in case it is open then it can be signified as a rectangular shape that has a length of 2r units and a breadth of h units.

As per the formula of the area of a circle, the area of the circular base of the mentioned cylindrical structure will be πr2. Because of two circular bases, the formula stands as πr2 + πr2 = 2πr2. At times, when the curved surface is opened in the space of two dimensions, a rectangle is formed. In this situation, the height and circumference of circular bases are the dimensions created by the rectangle. 

“Area of the curved surface = Height × Circumference”

CSA (Curved Surface Area) = h × πd = h * 2πr, as d = 2r, therefore, CSA =2πrh.

It is vital to add equation one with equation 2 to find out the total surface area of the cylindrical structure. 

Total surface area (TSA) = Area of circular bases + Curved surface area or 2πrh + 2πr2 or 2πr (h + r), therefore the concept of the formula is proved.

 Conclusion

The document is based on the total surface area of a cylinder and the entire discussion is on the formula that is used to calculate this aspect. This data will help in understanding the concept of total surface area in a better way in context to any shape and specific information has been also added in reference to the cylinders. It is necessary to add all the faces of a structure to calculate the total surface area and radius, height, side, axis, base are a number of attributes required to calculate this for a cylinder.