Before knowing how to calculate surface area of cylinder, let us know what a cylinder is. A cylinder is said to be a three dimensional object that has two bases separated by a finite distance. The surface of a cylinder is formed by the points at a fixed distance from the axis of the cylinder.
The total surface area of a cylinder is calculated as the sum of the surface area of the top and bottom of the cylinder and the surface area of the circular surface of the cylinder. The formula for calculating surface area of the cylinder is given as below,
As the top and bottom of the cylinder are the circular surfaces of equal dimensions, surface area of the top and bottom of the cylinder are given by the formula,
Area of top of the cylinder = π r2
Area of bottom of the cylinder = π r2
Adding both these areas we get,
Area of bases of a cylinder = 2 π r2
Area of the lateral surface or curved surface of a cylinder is given as,
Curved surface area of a cylinder = 2 π r h
Therefore,
Total surface area of a cylinder = Area of both the bases of the cylinder + Curved surface area of a cylinder
Total surface area of a cylinder = 2 π r2 + 2 π r h
Total surface area of a cylinder = 2 π r (r + h)
In the above formula,
- “π” is a constant(value of π = 3.14 or 22/7)
- “r” is the radius of base of the cylinder
- “h” is the height of the cylinder
Area of a cylinder is expressed in square units.
- To calculate area of a cylinder you will have to know the measures of the base and the height of the cylinder. You need not calculate the area of the bases and curved surface area separately; instead use the simplified formula that is given in bold case above.
Example:
Calculate the surface area of a sphere whose radius and height are 4.5 and 6.6 centimeters respectively.
Given that,
Radius = 4.5 cm
Height = 6.6 cm
Therefore,
Surface area of a cylinder = 2 π r (r + h)
Surface area of a cylinder = 2 × 3.14 × 4.5 × (4.5 + 6.6)
Hence,
Surface area of a cylinder = 313.686 cm2
If radius and height are given in different units then first convert them into compatible units. If you don’t know the conversion factors between different units then you can take help of online sources for this.
Area of cylinder can also be calculated using online calculators. They are very easy to use and display results within fraction of second when you enter the values of required fields in the text boxes and click on the calculate button.
Practice problems:
- Calculate curved surface area and total surface area of a cylinder whose radius is 12 m and height is 34.44 m.
- Calculate total surface area of a cylinder whose volume is 145.5 cm3 and height is 34 cm.( Volume of a cylinder = π r2)
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