Parametric Volumes of Revolution (Edexcel International A Level Maths): Revision Note

Parametric Volumes of Revolution

What is parametric volumes of revolution? 

• Solids of revolution are formed by rotating functions about the x-axis

• Here though, rather than given y in terms of x, both x and y are given in terms of a parameter, t

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  • Depending on the nature of the functions f and g it may not be convenient or possible to find y in terms of x

How do I find volumes of revolution when x and y are given parametrically? 

• The aim is to replace everything in the ‘original’ integral so that it is in terms of t

• For the ‘original’ integral and parametric equations given in the form  and use the following process

• STEP 1: Find dx in terms of t and dt

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• STEP 2: If necessary, change the limits from x values to t values using

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• STEP 3: Square y

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  • Do this separately to avoid confusing when putting the integral together
    

• STEP 4: Set up the integral, so everything is now in terms of t, simplify where possible and evaluate the integral to find the volume of revolution