You can find a volume of revolution around the y-axis by considering x as a function of y. The diagram shows a curve x = f(y). A small strip of height 𝛿y is rotated by 2π radians about the y-axis. The volume of the cylinder created will be πx²𝛿y since the radius is x and the height is 𝛿y

⇒ Also see our notes on:

• Volumes of Revolution Around the x-axis
• Adding and Subtracting Volumes
• Modelling with Volumes of Revolution