Right Circular Cylinder – Definition – Surface Area and Total Surface Area of a Right Circular Cylinder
Right Circular Cylinder
Surface Area of a Right Circular Cylinder
Definition:
Right Circular Cylinder
A Right Circular Cylinder is a three dimensional object, whose base is circle and the height (axis) is the line joining the centers of bases.
We take a rectangular sheet of a paper whose length is enough to go round the cylinder and covered cylinder with paper, and breadth of paper is equal to the height of the cylinder.
The area of the sheet gives us the curved surface area of the cylinder.
The length of the sheet is equal to the circumference of the circular base which is equal to 2𝝿r.
So, curved surface area of the cylinder
= area of the rectangular sheet = length x breadth
= perimeter of the base of the cylinder x h
= 2𝝿r x h
Therefore,
Curved Surface Area of a cylinder = 2𝝿rh
where r is radius of the base of the cylinder and h is the height of the cylinder.
Total Surface Area of Cylinder
Total surface area of a cylinder is equal to the sum of areas of all it’s surfaces, means outer surface of the cylinder plus top and bottom surface of the cylinder.
If the top and the bottom of the cylinder are also to be covered, then we includes two circles (circular regions) each of radius r, and area is 𝝿r2.
So, total surface area = 2𝝿rh + 2𝝿r2
=2𝝿r (r + h)
∴ Total Surface Area of Cylinder = 2𝝿r (r + h)
where h is height and r is radius of cylinder.