A solid of revolution is generated by revolving a plane area R about a line L known as axis of revolution in the plane. Below image shows an example of solid of revolution.
We shall calculate the volume of solid of revolution when the equation of the curve is given in parametric form and polar form.
 Parametric Form :
If the equation of curve in parametric form is given by:x= f(t) and y= g(t)
Where t varies from t_{1}to t_{2}, then the volume of revolution:

About xaxis –

About yaxis –

About xaxis –

Polar form:
Given the equation of curve in polar form as r=f(θ), where θ varies from θ_{1} to θ_{2}, the volume of revolution is calculated using the given formulas:
About the initial line OX i.e., xaxis (θ=0) –

About the line perpendicular to the initial line i.e. along OY (θ=π/2) –

About the initial line OX i.e., xaxis (θ=0) –
Let us see the following examples.
Example1:
Determine the volume of solid of revolution generated by revolving the curve whose parametric equations are –
X= 2t+3 and y= 4t^{2}9
About xaxis for t= 3/2 to 3/2.
Explanation :
We know that volume of solid revolved about xaxis when equation is in parametric form is given by
Using this value we get
Example2:
Find the volume of solid generated by revolving curve r= 2a cos θ about the initial line OX.
Explanation :
We know that volume of solid generated by revolving about OX in when equation is in polar form is given by
Also for OX, θ=0
So
Put
Using these values we get
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