$1$ . $\newline$ These two solids have matching cross-sectional areas at every plane parallel to the base.. Do they have the same volume? $\newline$ $4$ . Finish the sentence: $\newline$ $2$ . Cavallerl sald two sollds will have the same volume If they have the same...

Full solution

1

\newline

These two solids have matching cross-sectional areas at every plane parallel to the base.. Do they have the same volume?

\newline

4

. Finish the sentence:

\newline

2

. Cavallerl sald two sollds will have the same volume If they have the same...

Understand Principle: Understand the principle of Cavalieri's Principle. $\newline$ Cavalieri's Principle states that if two solids have the same height and the same cross-sectional area at every level, then they have the same volume.
Apply Cavalieri's Principle: Apply Cavalieri's Principle to the given problem. $\newline$ Since the two solids have matching cross-sectional areas at every plane parallel to the base, according to Cavalieri's Principle, they will have the same volume if they also have the same height.
Determine Height: Determine if the solids have the same height. $\newline$ The problem does not provide information about the height of the solids. To conclude that they have the same volume, we need to know if their heights are the same.
Answer Question: Answer the question based on the information given. $\newline$ Without information about the height of the solids, we cannot definitively say that they have the same volume. However, if they do have the same height, then they would have the same volume.
Complete Sentence: Complete the sentence based on Cavalieri's Principle. $\newline$ Cavalieri said two solids will have the same volume if they have the same height and cross-sectional area at every level.