Formula of CSA of Cylinder: Definition, Examples, Surface Area, Derivation, TSA, and Differentiation

Formula of CSA of Cylinder Overview

The Surface Area of a Cylinder is classified into two types: Curved Surface Area (CSA) and Total Surface Area (TSA). In geometry, the area of any form is the area it occupies in a plane. A cylinder can have two surfaces: one with a curved surface and one with two round bases. The area of both circular bases is the same.

What is a Cylinder?

A cylinder is a three-dimensional solid structure with two parallel circular bases linked at a constant distance by a curving surface. It's also possible to see it as a stack of circular discs. The axis of the cylinder is the line segment connecting the centers of two circular bases. The distance from the axis to the outer curved surface is known as the cylinder's radius (r), and the perpendicular distance between the two parallel circular bases is known as the cylinder's height (h). 

Examples of Cylinder

There are several instances of cylindrical-shaped items that we encounter in our daily lives which are as follows-

1. Candles
2. Pipe
3. Water Tanks
4. Wells

What is the Surface Area of the Cylinder?

The area of any shape in geometry is the region it covers in a plane. A cylinder is made up of two types of surfaces: curved surfaces and circular bases. Both circular bases have the same area. The cylinder's surface area may be divided into two types-

1. Curved Surface Area (CSA) 
2. Total Surface Area (TSA)

What is the CSA of a Cylinder?

A cylinder's curved surface area (CSA) is the area covered by its curved surface solely. The curved surface area of a cylinder is determined using the formula if the radius of the base of the cylinder is 'r' and the height of the cylinder is 'h'.

Formula of CSA of Cylinder

Cylinder curved surface area (CSA) = 2 𝜋rh

where,

r = radius of the cylinder

h = height of the cylinder

π = 22/7 or 3.14

Example for Formula of CSA of Cylinder

Find the curved surface area of a cylinder with a radius of 7 cm and a height of 14 cm.

Solution: CSA of cylinder = 2 𝜋rh

By placing the values,

r = 7 cm

h = 14cm

We get-

CSA = 2 𝜋rh

        = 2 x 3.14 x 7 x 14 

         = 6.28 x 98 cm²

         = 615.44 cm²

Therefore, the curved surface area of a cylinder is 615.44 cm².

Derivation of the Formula of CSA of Cylinder

The following is the derivation of the formula of CSA of a cylinder-

1. Consider the radius "r" and height "h" of a solid cylindrical form. 
2. Take a rectangular sheet and wrap it around the cylinder to get the formula for the curved surface of the cylindrical body. 
3. Cut the top and bottom edges to fit the form of this cylinder. 
4. The curved surface of the cylinder is represented by the area of this rectangular piece of paper. The area of the cylinder's curved surface equals the area of the rectangular sheet.
5. As a result, the area of the curved surface equals the length of the rectangle multiplied by the breadth of the rectangle.
6. We may deduce from this that,
7. The length of the rectangle equals the circumference of the cylinder's base = 2πr
8. The width of the rectangle equals the height of the cylinder =h
9. The area of the curved surface equals the area of the rectangle = length x width

                                                                                                      = 2πrh

Read more about the Perimeter of Cuboid, Volume of a Cuboid, TSA of Cuboid and Area of a Parallelogram.

Formula of TSA of Cylinder

A cylinder's total surface area is defined as the sum of the areas of its curving surface and two circular bases. TSA of a cylinder of radius 'r' and height 'h' is given by-

Total cylinder surface area (TSA) = area of curved surface + area of its two circular bottoms

 or, 

Cylinder TSA = Cylinder CSA + area of its two circular bases

= 2rh + 2r²square units

TSA of a cylinder = 2r (h + r) square units

Related Articles-

Who invented Math?

Difference Between Fraction and Rational Numbers

Father of Mathematics

Difference Between Place and Face Value

Difference between CSA and TSA of a Cylinder

The primary distinction between the Total Surface Area (TSA) and Curved Surface Area (CSA) of a Cylinder is that TSA is the sum of the areas of all the cylinder's surfaces, including the two circular bases and the curved surface, whereas CSA is the area of the curved surface only. The following table gives the difference between curved surface area and the total surface area of a cylinder-

Read more about the Difference Between Cube and Cuboid.