Fraser, Georgina, and Owen are each trying to build the tallest snowman.
- Fraser: "Fewer snow spheres should be taller. I will stack 2 spheres of equal radii."
- Georgina: "I disagree, I think more snow spheres will be taller. I will stack 10 spheres of equal radii."
- Owen: "It doesn't matter how many spheres you make. I'll make 6 spheres of equal radii and all three of our snowmen will be the same height."
Who is correct?
If they all have the same volume of snow, which snowman is tallest?
Details and Assumptions:
- Each child has the same volume of snow.
- Each sphere is perfectly spherical, and is tangential to the spheres above and below it. The bottom spheres sit on level ground.
- Assume that each child can stack the spheres so that they will not topple or collapse under the weight of the spheres above.