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For a cylinder, we need to calculate the surface area of top, bottom and sides.
Area of the top = pi * r^{2}
Area of the bottom = pi * r^{2}
Area of the side = 2* pi * r * h
Where r=radius of the cylinder, h = height of the cylinder and pi=3.14
So, area of the cylinder = (2 * pi * r^{2 }) + (2 * pi * r * h)

In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object.
(h is the height of the cylinder, r is the radius of the top)
Surface Area = Areas of top and bottom +Area of the side
Surface Area = 2(Area of top) + (perimeter of top)* height
Surface Area = 2(pi r^{ 2}) + (2 pi r)* h
In words, the easiest way is to think of a can. The surface area is the areas of all the parts needed to cover the can. That's the top, the bottom, and the paper label that wraps around the middle.
You can find the area of the top (or the bottom). That's the formula for area of a circle (pi r^{2}). Since there is both a top and a bottom, that gets multiplied by two.
The side is like the label of the can. If you peel it off and lay it flat it will be a rectangle. The area of a rectangle is the product of the two sides. One side is the height of the can, the other side is the perimeter of the circle, since the label wraps once around the can. So the area of the rectangle is (2 pi r)* h.
Add those two parts together and you have the formula for the surface area of a cylinder.
Surface Area = 2(pi r^{ 2}) + (2 pi r)* h

Area is the region occupied by an object in the observed place.
Two different types of areas for cylinder can be dusussed they are CrossSectional area and Surface area.
We need to know follwoing details to calculate area of cylider.
pi= constant whose value equals(22/7)
r= radius of the cylinder.
h= height of the cylinder.
1. CrossSectional area of Cylinder = pi*r^{2}*h
2. Surface area = (2 * pi * r^{2 }) + (2 * pi * r * h)

Here are some visuals to help you understand the area of a cylinder.

A cylinder has 3 faces in total, so when we have to find its area, it is the sum of all these three faces. The cylindrical part and the two circular parts. Top and the bottom are circular in shape. So the total area is A= ( π r^{2 }+ π r^{2 })^{ }+ ( 2 π r h) = 2 πr^{2} +2 π r h= 2 πr(r+h)

Total Surface Area of a Cylinder
Consider a cylinder of radius r and height h. The total surface area (TSA) includes the area of the circular top and base, as well as the curved surface area (CSA).
The total surface area (TSA) of a cylinder with radius r and height h is given by
Suggested reading…
Calculate the surface areas of cylinders, cones and spheres
How do I find surface area of spheres, cones and cylinders?
Just use these simple equations;
Formula for Surface Area :
Cylinder = 2πr² + 2πrL (L is the length of the cylinder)
Cone = πr² + πrL (L is the length from the point of the cone to the edge of the base)
Sphere = 4πr2
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