Math
Surface Area of a Cylinder Formula & Volume of a Cylinder Formula
Table of Contents
Surface Area of a Cylinder Formula
A cylinder is a 3dimensional structure with a circular base. It can also be taken as the set of circular disks which are stacked together one by one. Now take an example, where you are interested in painting the cylinder faces within the container. So, what you need to know exactly here? First of all, you need to calculate the quantity of paint for the container. For this purpose, you have to calculate the total surface area of the cone that is given as the sum of areas of a cylinder.
To make this concept little more interesting for you, let us take a cylinder with radius r and height h units. The circular base of the cylinder will be transformed to a rectangle with length ‘2𝝿r’ and height ‘h’ units. It can be given as shown in the figure below.
And the surface area of a cylinder formula in mathematics is written as –
\[\large Surface\;Area\;of\;a\;Cylinder=2\pi r(r+h)\]
And the curved surface area of a cylinder formula can be given as –
\[\large Curved\;Surface\;Area\;of\;a\;Cylinder=2\pi rh\]
Where,
r is the radius of the cylinder having circular base.
h is the height of the cylinder with parallel faces.
The volume of a Cylinder Formula
As we have already mentioned that cylinder is simply set of circular disks which are stacked together one by one. So, we need to check the space occupied by these discs and this is possible by computing volume of a cylinder. For example, if circular discs are stacked up to the height h then cylinder volume formula could be written as –
\[\large Volume\;of\;a\;Cylinder=\pi r^{2}h\]
Where,
R is the radius of the cylinder having circular base and h is the height of the cylinder with parallel faces. In our day to day life too, we came across different types of situations where this is necessary to handle circular objects.
The formula is suitable to calculate the capacity of such type of cylindrical objects. The formulas are also helpful in designing cylindrical containers flasks, bottles, perfume bottles etc. This is easy to calculate the volume of a cylinder if you know the radius and the height of the cylinder.
The Radius of a Cylinder Formula
To calculate the radius of a cylinder, you don’t have to put any extra efforts but rearrange the formula and put given values accordingly. In the end, you need to take the square root on the radius and this would be the final outcome.
\[\large Radius\;of\;a\;Cylinder=\sqrt{\frac{V}{\pi h}}\]
Where,
V is the Volume of the cylinder.
h is the height of the cylinder with parallel faces.
The perimeter of Cylinder Formula
In most of the cases when you need to find the perimeter of a cylinder then diameter and height are given for that particular problem. The Perimeter of a cylinder is the outline of a twodimensional shape. But cylinder is a 3dimensional shape so how to calculate the perimeter here. This is possible by creating a projection on the base and reduce the shape to a rectangle. Now calculation of perimeter is possible in case of 3dimensional cylinder too. The formula for the perimeter of a cylinder is given as –
\[\large Perimeter\;of\;a\;Cylinder=(2 \times d) + (2 \times h)\]
Where,
d is the diameter of the cylinder having circular base and h is the height of the cylinder with parallel faces.
Question 1: What will be the surface of the cylinder with height 10 cm and diameter of the base is 12 cm.
Solution:
Given,
Height = 10 cm
Diameter = 12 cm
Radius = 6 cm
surface Area of Cylinder = 2πr(r+h)
= 2 X 3.14 X 6 (6+10)
= 12 X 3.14 X 16
= 602.88 cm^{2}
Question 2: How many litres of water can a cylindrical water tank with base radius 20 cm and height 28 cm hold?
Solution: Given,
Base radius of the cylindrical water tank, r = 20 cm
Height of the cylindrical water tank, h = 28 cm
Volume of the cylindrical water tank = πr^{2}h
Volume of the cylindrical water tank = 3.14 X 20^{2}28 = 35200
1 cubic centimeter = 0.001 litre =1 X 10^{3} litre
∴ 35200 cubic centimeter = 35200 X 10^{3} = 35.2 litres
The cylindrical water tank can hold 35.2 litres of water

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