Question
Cavalieri’s Principle states that any two objects with the same cross sectional areas and heights must have the same volume.
Cavalieri’s Principle states that any two objects with the same cross sectional areas and heights must have the same volume.
False - the cross sectional areas are not relevant
True
False - only the slant height is relevant
False - even if they have the same cross sectional areas and heights, they cannot have the same volume.
Cavalieri’s Principle states that any two objects with the same cross sectional areas and heights must have the same volume.
False - the cross sectional areas are not relevant
True
False - only the slant height is relevant
False - even if they have the same cross sectional areas and heights, they cannot have the same volume.
Answers
GPT-4o
True
Cavalieri’s Principle indeed states that if two objects have the same height and their cross-sectional areas are equal in all corresponding planes parallel to a chosen base, then the volumes of the two objects are equal. Therefore, the principle directly relates the equality of cross-sectional areas and height to the equality of volumes.
Cavalieri’s Principle indeed states that if two objects have the same height and their cross-sectional areas are equal in all corresponding planes parallel to a chosen base, then the volumes of the two objects are equal. Therefore, the principle directly relates the equality of cross-sectional areas and height to the equality of volumes.