What is a volume of revolution around the?x-axis?

• A?volume?of?revolution?is the volume of this solid formed

How do I find the volume of revolution around the?x-axis?

• The formula may look complicated or confusing at first due to the?y?and dx
  • remember that?y?is a function of?x
  • once the expression for?y?is substituted in, everything will be in terms of?x
• π is a constant so you may see this written either inside or outside the integral
• This is?not?given in the formulae booklet
  • The formulae booklet does list the volume formulae for some common 3D solids – it may be possible to use these depending on what information about the solid is available

How do I solve problems involving volumes of revolution around the?x-axis?

• Visualising?the solid created is helpful
  • Try sketching some functions and their solids of revolution to help
• ?STEP 1?Square?y
  • Do this first without worrying about π or the integration and limits
• STEP 2?Identify the limits?a?and?b?(which could come from a graph)
• STEP 3?Use the formula by evaluating the integral and multiplying by π
  • The answer may be required in?exact form?(leave in terms of π)
    • If not, round to?three significant figures?(unless told otherwise)
• Trickier questions may give you the volume and ask for the value of an unknown constant elsewhere in the problem

What is a volume of revolution around the?y-axis?

• A?volume?of?revolution?is the volume of this solid formed

How do I find the volume of revolution around the?y-axis?

How do I solve problems involving volumes of revolution around the?y-axis?