IB DP Maths: AA HL复习笔记5.9.5 Modelling with Volumes of Revolution

When would volumes of revolution need to be added or subtracted?

How do I know whether to add or subtract volumes of revolution?

How do I solve problems involving adding or subtracting volumes of revolution?

• Visualising the solid created becomes increasingly useful (but also trickier) for shapes generated by separate volumes of revolution
  • Continue trying to sketch the functions and their solids of revolution to help

STEP 3

The answer may be required in exact form

What is meant by modelling volumes of revolution?

• Many everyday objects such as buckets, beakers, vases and lamp shades can be modelled as a solid of revolution
• The volume of revolution of the solid can then be calculated
• An object that would usually stand upright can be modelled horizontally so its volume of revolution can be found

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 handle on a bucket would not be included
• The thickness of the solid is negligible relative to the size of the object
  • thickness will depend on the purpose of the object and the material it is made from

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 fomulae
• The volume of revolution may involve adding or subtracting partial volumes
• Questions may ask related questions in context
  • g. A question about a bucket may ask about its capacity
    • this would be measured in litres
    • so a conversion of units may be required
    • (100 cm³ = 1 litre)