Surface area is the amount of space covering the outside of a three-dimensional shape.
A Cylinder is a 3D structure having round or circular bases parallel to each other. A cylinder has no vertices. Surface area of a cylinder refers to the area occupied by its surface in a three-dimensional space.
The Surface Area of Cylinder = Curved Surface + Area of Circular bases
Formula used to calculate the ‘Surface Area of a Cylinder’ is –
Surface area of a cylinder = 2 πr (h+r) sq. unit.
Here π = 3.142 or 22/7, r = radius of the cylinder and h = height of the cylinder.
Now as you have an idea on how to calculate the surface area of a cylinder, let’s have a glance at the examples -
Example 1:
Find the Curved surface area of a cylinder of radius 7 cm and height 14 cm.
Solution: The curved surface area of a cylinder can be calculated using the formula, CSA = 2πrh. After substituting the value of r = 7, h = 14, we get: CSA = 2πrh = 2 × 3.14 × 7 × 14 = 615.8 cm^{2}
Example^{ }2:
What will be the surface of the cylinder with height 10 cm and the diameter of the base is 12 cm.
Solution:
Given, Height = 10 cm Diameter = 12 cm
Hence, Radius = d/2 = 12/2 = 6 cm
According to the formula:
TSA = 2πr(r+h)
2×3.14×6(6+10)
=602.88cm^{2}
Now let us see how to calculate the height of a cylinder if the TSA is given.
Example 3:
Find the height of a cylinder if its total surface area is 2552 in^{2 }and the radius is 14 in.
Solution
Given:
TSA = 2552 in^{2}
Radius, r = 14 in.
But, TSA = 2πr (h + r)
2552 = 2 x 3.14 x 14 (14 + h)
2552 = 87.92(14 + h)
Divide both sides by 87.92 to get,
29.026 = 14 + h
Subtract by 14 on both sides.
h = 15
Hence, the height of the cylinder is 15 in.
The curved surface area is defined as the area of only curved surface, leaving the circular top and base.
Consider a cylinder having a height ‘h’ and base radius ‘r’.
The curved surface area of a cylinder is given as-
C.S.A. =2πrh
Example- Consider a curved surface area of a cylinder having height of 5 cm and diameter of base to be 2 cm.
Solution- Given h = 5 cm, and d = 2 cm,
Therefore, r = 1 cm
C.S.A. = 2πrh=2π*1*5=10π
By the formula of area of the circle, we know,
Area of the circular base of cylinder = πr^{2}
Since there are two circular bases, the area of both the circular bases = πr^{2 }+ πr^{2} = 2πr^{2}……….. (1)
Now, from the figure, you can see that the curved surface of the cylinder in two-dimension space forms a rectangle when opened. Hence, the height and circumference of the circular bases are the dimensions of the rectangle formed from it. Therefore,
Area of the curved surface = Height × Circumference
Curved Surface area = h × πd = h × 2πr (since d = 2r)
CSA = 2πrh …………….(2)
By adding equation 1 and equation 2, we get the total surface area, such that;
Total Surface area = Curved Surface area + Area of Circular bases
TSA = 2πrh + 2πr^{2}
By taking 2πr as a common factor from RHS, we get;
TSA = 2πr (h + r)
Therefore, Surface area of a cylinder = curved surface + area of circular bases
In terms of π,
Surface area of a cylinder = 2 πr (h+r) sq unit.
The sum of the areas of the two circles and the rectangle is:
A= πr^{2}+ πr^{2}+2πrh
By combining like-terms, we can simplify this equation to:
A=2πr(r+h)
Here, A is equal to area, pi is equal to 3.14, r is equal to the radius, and h is equal to the height
Q2.What is the surface area formula?
Surface area is the sum of the areas of all faces (or surfaces) on a 3D shape.
Surface Area Formulas:
Shape |
Lateral Surface Area (LSA) |
Total Surface Area (TSA) |
Cuboid |
2h(l + b) |
2(lb + bh + lh) |
Cube |
4a^{2} |
6a^{2} |
Right Prism |
Base perimeter × Height |
LSA + 2 (area of one end) |
Right Circular Cylinder |
2πrh |
2πr(r + h) |
Right Pyramid |
(1/2) Perimeter of base × Slant Height |
LSA + Area of Base |
Right Circular Cone |
πrl |
πr(l + r) |
Solid Sphere |
4πr^{2} |
4πr^{2} |
Hemisphere |
½ × 4 × πr^{2} |
3πr^{2} |
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