Solution:

(a) Buckminsterfullerene is a carbon allotrope with 60 carbon atom clusters linked together to create spherical molecules. Nothing is left behind when it burns to generate carbon dioxide when heated. This demonstrates that it is formed entirely of carbon, similar to diamond and graphite.

(b) Diamond is used to make cutting tools, but graphite is not since diamond is a hard substance while graphite is soft.

(c) Dry cell electrodes are made of graphite rather than diamond since graphite is a good conductor of electricity while diamond is a poor conductor.