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Australian AMC 2013 - Senior Question 25

AMC AUSTRALIA · Australian AMC 2013 - Senior

Question 25

Two spheres, one of radius 1 and the other of radius 2, touch externally at P. A plane through P cuts the volume of the shape formed by these two spheres in the ratio 1 : 2. In what ratio does this plane cut the volume of the smaller sphere?

Question illustration
  1. 1 : 2
  2. 4 : 9
  3. 1 : 3
  4. 4 : 11
  5. 2 : 5