Question

Cavalieri’s principle states that two solids with equal heights and cross sectional volumes at every level have equal areas

True or false

Answer 1

False

Explanation:

We are given a statement regarding Cavalieri's principle.

The given statement is false.

CavalierIi's principle.

• Two solids of equal altitude or height, the cross-sections made by planes parallel to the base of the solid are always equal, then the volumes of the two solids are said to be equal.
• If two solids or 3-D figures are considered between two parallel planes. If the cross sectional area formed by the intersection of the planes and the solid figure are equal, then the two solids have equal volumes.
• The given equation states the equality of cross sectional area in place of the volume.
• Thus, the given statement is false.

Answer 2

False

Explanation:

we know that

The Cavalieri's principle states that if two or more figures have the same cross-sectional area at every level and the same height, then the figures have the same volume.

see the attached figure to better understand the problem