Hello, I am trying to answer this Geometry question, but I am not sure if it makes sense. Can any of you confirm that my reasoning is logically correct?

Question

anonymous · Answer

5. In Giant Gum, the gum is shaped like a pyramid. What shape do you think would best fit into the container (choose a shape other than a pyramid). Explain why the shape you chose was better and back up your answer with proof such as calculations and writing.

I think a cone would best fit into the sphere container because the round surface of the cone would minimize the spaces between the cone, the sphere, and other cones. Also, the base area of the cone is (pi)(r squared), instead of  (b squared), the base area of the pyramid. You can see the advantage by using 1 inch as an example base length. For the pyramid, you would simply get 1 square inch. For the cone, you would get (3.14)(.5 squared) -> (3.14)(.25) -> .75 square inches. This shows that the cone would still be smaller with the same dimensions.

anonymous · Answer

@Hero

hero · Answer

Doesn't make much sense to me either. There seems to be a flaw in the wording.

anonymous · Answer

I assumed that they were trying to make me choose the shape that would be able to make the most contact in the sphere, leaving little to no empty space. That's why I chose the cone because of its round surface.

phi · Answer

makes sense to me.

hero · Answer

If they're referring to a sphere container, then perhaps spherical balls would best fit into it.

hero · Answer

The question by itself without referencing what kind of container it is, would not make sense @phi

anonymous · Answer

Yeah, they referenced a sphere container in the previous question, but they didn't mention it in this one, so I just assumed they were referring to the same one. But referring to your statement about spherical balls being the best fit, wouldn't that leave a lot of empty space between the spheres. That's why I thought that a cone would be able to make the most contact in terms of surface area with other cones in the sphere. Or is that bad reasoning?

hero · Answer

Of course that would depend on the size of the spherical balls or cone-shaped gum. The smaller the better.

phi · Answer

Your reasoning is ok

anonymous · Answer

Okay, that makes sense. Thank you, @Hero and @phi .