Surface Area of Cylinder

Cylinder

Cylinder is a three-dimensional shape with two parallel circular discs or bases separated by a certain distance. At a fixed distance from the centre, the two circular bases are connected by a curved surface. The distance between the two parallel circular bases of the cylinder is referred to as the height of the cylinder.

Parts of Cylinder

Cylinder Faces, Vertices, and Edges

Faces: A cylinder has 3 faces in total (2 flat circular faces + 1 curved face)
Edges: A cylinder has 2 edges (one at the top and one at the bottom)
Vertices: A cylinder has 0 vertices (as the two edges of the cylinder never meet)

Area of Cylinder

A cylinder has two kinds of surface areas:
1. The curved surface area or the lateral surface area
2. Total surface area.

Curved Surface Area (CSA) or Lateral Surface Area (LSA)

The curved surface area, or lateral surface area of a cylinder, is the space enclosed between the two parallel circular bases.
Curved Surface Area (CSA) = 2πrh square units

Where,
r is the radius of the cylinder.
h is the height of the cylinder.

Total Surface Area (TSA)

The total surface area of a cylinder is the total area enclosed by a cylinder, including its bases. A cylinder has a lateral surface and two bases that are parallel and identical. Therefore, the total surface area of a cylinder is the sum of the area of the curved surface or lateral surface and the areas of the two circular bases.
We know that,
Curved Surface Area (CSA) = (2 πrh) square units
Area of a Circle = πr² square units
Total Surface Area (TSA) of a cylinder = Curved Surface Area + 2(Area of a circle)
TSA = 2πrh + 2πr² = 2πr(h + r) square units

Where,
π (pi) is a mathematical constant (approximately equal to 3.14)
r is the radius of the circular base
h is the height of the cylinder