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Important Cylinder Formulas
Using the three main factors of a Cylinder, we get the three important formulas of Cylinder.
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Total Surface Area of Cylinder
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Lateral surface Area of Cylinder
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Volume of Cylinder
1. Total Surface Area of Cylinder – The Total Surface Area of a Cylinder is the area which covers the space between the two parallel circular bases(Curved surface area) and the area of the two bases(Area of Circles).
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Total Surface Area of a Circle = 2πrh + 2πr2 = 2πr(h+r) square units, where h is the height or distance between the two axis and r is the radius from the axis to the outer boundary of the circle. |
2. Curved Surface Area
The area of the space covered between the two circular bases in the cylinder is called the Curved Surface Area or Lateral Surface Area of a Cylinder.
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Curved Surface Area, C.S.A = 2πrh square units, where r is the radius of the two circular bases and h is the height of the distance between the two circular bases. |
3.Volume of a Cylinder: The space inside any three dimensional object is known as its volume. In a simpler way, the total amount of water which can be stored in a cylinder is its volume.
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Volume of a Cylinder, V = πr2h cubic units, where h is the height of the cylinder and r is the radius of the circular base of the cylinder. |
What are the Properties of a Cylinder?
There are many important properties of Cylinder. Few of them are given below.
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The two circular bases of a Cylinder are always parallel and congruent.
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A right cylinder is formed when the axis forms a right angle with the bases of the cylinder which are opposite to each other.
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Similarity between a prism and a cylinder is that both have the same cross section at each point.
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Contrary to the Right Cylinder, if the two bases of the cylinder are not over each other and the axis do not make a right angle with the two bases, that cylinder would be considered as the Oblique Cylinder.
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The cylinders which have circular bases are known as circular cylinders and cylinders having elliptical bases are known as Elliptical Cylinders.
Real Life Examples of Cylinder
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Pipe
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Water Tank
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LPG Cylinder
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Batteries
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Water Glass
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Test Tube etc
Problems
Question 1: If the height of the cylinder is 10 cm, and radius is 7cm, Find it’s Total surface area?
Solution: The total surface area of the cylinder is equal to 2πr(r+h) square units
It is given that r = 5 cm and h = 10 cm.
So, the total surface area of the Cylinder is 2 * 22/7 * 7* (7 + 10) = 2 * 22 * 17 = 748 cm2
Question 2: Find the volume of the cylinder having height 6 cm and diameter 10cm?
Solution: The volume of a cylinder is its capacity to contain the water in it.
Given, r = 5cm (d/2) as d= 10cm
The formula to find the volume of the Cylinder is πr2h = 3.14 * 5 *5 * 6 = 471 cm3