We all see many cylindrical objects around us.
A thermos flask, a cold-drink can and packets of biscuits, all are cylindrical shaped.
These cylinders have two circular surfaces at the top and bottom of the cylinder.
And between these two plain circular surfaces, we have a curved body of the cylinder.
So, in a closed cylinder, we have three surface. Two circular and one covered.
Now, Suppose if we want to gift a deodorant bottle which is in cylindrical shape to our friend so we need to wrap it up.
If we want to spend the minimum of the paper required for the wrapping, we can cover the three surfaces separately.
The top and bottom cover of the cylinder will be circular and we will require a rectangular sheet to cover the curved surface.
Then the amount of paper required to cover this cylinder bottle will be equal to the surface area of the cylinder.
Let’s discuss the surface area of the cylinder.
The surface area of the cylinder is consists of two types of surface. Plain circular and curved.
If we have an open cylinder, all we have will be a curved surface.
And the surface area of this curved surface is called the curved surface area.
If we consider the surface area of both the circular surface along with the curved surface, it would be called the total surface area of the cylinder.
Let’s find the curved and total surface area of the cylinder.
Let’s take a closed cylinder with a base of radius say and let the height of the cylinder be .
The area of the top and bottom of the cylinder will be simply the area of the circles of radius .
Now, the lateral surface of the cylinder is curved upon these circular bases.
So, the length of the rectangular sheet used to make this curved surface will be equal to the circumference of the bases.
As the height of the cylinder is , the area of the curved surface will be given by,
So, the curved surface area of a cylinder is give by
And the total surface area of the cylinder is given by
A cylinder consists of three surface. Circular top, circular bottom and curved lateral surface.
The lateral surface of the cylinder is made of a rectangular sheet and its area is given by.
The total surface area of the cylinder and its curved surface area is given by