What is meant by modelling with volumes of revolution??

• Many every day objects such as buckets, beakers, vases and lamp shades can be modelled as a?solid?of?revolution
• This can then be used to find the?volume?of the?solid?(volume of revolution) and/or other information about the solid that could be useful before an object is manufactured
• Modelling with volumes of revolution could involve rotation around the?x-axis?or?y-axis?so ensure you are familiar with both

What modelling assumptions are there with volumes of revolution?

• The solids formed are usually the?main?shape?of the?body?of the?object
  • For example, the handles on a vase would?not?be included
  • The lip on the top edge of a bucket would?not?be considered
• A common question or?assumption?concerns the?thickness?of a container
  • The thickness is generally ignored as it is relatively small compared to the size of the object
    • thickness will depend on the purpose of the object and the material it is made from
  • Some questions may refer to the solid formed being the ‘inside’ of an object or refer to the ‘internal’ dimensions
  • If the thickness of the material is significant it would involve two related solids of revolution (Adding & Subtracting Volumes)

How do I solve modelling problems with volumes of revolution??

• Visualising?and sketching the solid formed can help with starting problems
• Familiarity with applying the volume of revolution formulae for rotations around both the?x?and?y?axes

• The volume of a solid may involve adding or subtracting different volumes of revolution
  • Subtraction would need to be used for solids formed from areas that do not have a boundary with the axis of rotation
• Questions may go on to ask related questions in context so do take notice of the context
  • A question about a?bucket?being formed may ask about its?capacity
• This would be measured in?litres?so there may also be a mix of?units?that will need conversion (e.g. 1000cm³?= 1 litre)