Parametric Volumes of Revolution (Edexcel International A Level Maths) : Revision Note
Did this video help you?
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
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
STEP 2: If necessary, change the limits from x values to t values using
STEP 3: Square y
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
Worked Example

Examiner Tips and Tricks
Avoid the temptation to jump straight to STEP 4
There could be a lot to change and simplify in exam style problems
Doing each step carefully helps maintain high levels of accuracy
You've read 0 of your 5 free revision notes this week
Sign up now. It’s free!
Did this page help you?