Question

Use Cavalieri’s principle to compare the volume of the cone and triangular pyramid.

Answer 1

The volume of the 2 objects will equal only if:
the solids of equal height made by the same parallel and same distance from their bases = same volume of the two bases.

Answer 2

Cavalieri principle states that:

" If, in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal "

Hence here the given two solids are cone and triangular pyramid.

Hence if the two solids have same altitude or height, the sections made by planes parallel to and at the same distance from their respective bases will be equal then the volume of the given two solids will also be equal.