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Surface Area of the Body (Investigation)



  • To practice calculating surface area.
  • To practice estimation of surface area.
  • To use surface area to solve real-world problems.


Suppose you are sitting in the emergency room of a hospital. All of a sudden, you overhear two nurses talking about the next patient that is about to be brought in.

The first nurse says, “He’s completely burned! Do we have enough skin left in the skin graft bank for an adult?” The second nurse then replies, “There are $140$140 square metres left.” 


  1. From listening to this conversation you found out:
    • Patient is an adult male
    • Patient is completely burned
    • Skin graft bank contains $140$140 square metres of skin 
  2. Should you be worried about the patient? Work on your own or in small groups to determine if the hospital has enough skin left in the skin graft bank to treat the patient. Collect any materials you may need to create an estimate. Explain the method you used to reach this answer.
  3. Compare with a friend! Did they use a different method to estimate the amount of skin the man will need? Compare and contrast the different methods.
  4. Do you think one method may have been slightly more effective than the other?
  5. How close was their estimate to yours?
  6. The surface area of your body is given by the formula $A=(3/5)h^2$A=(3/5)h2 where $h$h is your height given in metres. Use this to calculate how much skin the man actually has. 



Deduce and use formulae to find the perimeters and areas of polygons and the volumes of prisms

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