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MATHEMATICS - CASE STUDY

    Introduction



Inscribe Cylinder in a Sphere
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While repairing an old washing machine, Wisdom finds a cylinder balance weight needs to be replaced. In order to save money, Wisdom decides to make this part by cutting a steel sphere. He wants the cylinder balance weight heaviest.

What is known:

  • The radius of the sphere is 0.05 m.
  • The mass density of this sphere is 7,900 kg/m3.
  • The cylinder is inscribed in the sphere.
  • The weight of the cylinder, w, is determined by its mass density, ρ, and volume, v.
     
    Questions

 

 

What can the maximum weight the cylinder be?

     
    Approach


 
  • Find the volume that can be inscribed in the sphere.
  • Using the second derivative test to verify the volume is maximum.