In mathematics, we have two different kinds of figures. Namely - Plane shapes and solid shapes. The solid shapes are three-dimensional. A cylinder is one among them. Several examples were available in our daily life, like gas cylinders, water tanks, cylindrical flasks, etc. Let's see the volume of a cylinder formula with the help of the formula area of the cylinder and the volume of the circle formula.
Volume of a Cylinder
The formula for the volume of a Cylinder helps to calculate the capacity and space available in it. If we observe the structure of a cylinder, it has a curved surface in the middle and circular faces at ends. First, we need to know the formula area of cylinder and the volume of circle formula. The summation of these two formulae can easily provide the volume of a cylinder formula.
Derivation of Formula
We need to consider the formula area of the cylinder for deriving the volume of cylinder formula.
If two circular surfaces are packed one upon the other with the support of a curved surface in the middle, then it is known as a cylinder. To get the formula for the volume of a cylinder, let's find the volume of each surface separately.
Let us assume that 'h' is the height of a curved surface.
We know that the formula for the area of a circle is πr².
By adding these two, we will get the formula of the cylinder.
The volume of cylinder = πr²h
Where r - radius of the circle.
Hence the product of height with the area of the circle gives the volume of the cylinder. It is also known as the volume of the right circular cylinder.
∴ Volume of a Cylinder = πr²h
Relation Between Cone and Cylinder
Cone and cylinder both have circular faces. So both volumes require an area of a circle formula. Here also, the height 'h' is considered for the Cone.
Representation of the formulae for the volume of Cone and cylinder are -
Volume of a Cylinder = πr²h
The volume of a Cone = ⅓(πr²h)
Hence the volume of circle formula is derived. It helps find the capacity of a container, perfume bottle, cylindrical flasks in chemical labs, water tanks, etc., easily. Also, the space occupied in it becomes simple with this formula.