Cavalieri's principle states that two solids with equal heights and cross-sectional volumes at every level have equal areas.A.TrueB.False

Answer

Cavalieri's principle indeed states that if two solids have the same height and the cross-sectional areas at every height are equal, then the volumes of the two solids are also equal.

In this context, the statement in question seems to incorrectly refer to "areas" rather than "volumes". The principle specifically applies to volumes rather than just areas. Therefore, in response to the given statement:

A. True would be a misunderstanding of the principle as it pertains strictly to volumes, not areas.

The correct understanding is:

• If two solids have equal heights and equal cross-sectional volumes at every level, they will have equal volumes, not areas.

Final Answer

B. False