Question

consider the following cylinder and cone.
marcel tried to use cavalieri’s principle to show that the two figures have the same volume.
“the base areas are the same. therefore, corresponding cross - sections have the same area. so the volumes must be the same.”
what is the first mistake marcel made?
choose 1 answer.
a the base areas are not the same.
b it isn’t true that corresponding cross - sections have the same area.

Explanation:

Cavalieri's principle requires that all corresponding cross-sections (not just the bases) have equal area for volumes to be equal. For the cone, cross-sections parallel to the base shrink in area as you move toward the apex, while the cylinder's cross-sections stay the same area as the base. Marcel incorrectly claimed corresponding cross-sections have equal area; the base areas are the same here, so his first mistake is the false claim about cross-section areas.

Answer:

B. It isn't true that corresponding cross-sections have the same area.