For the solids show, choose all the statements that will be true if we can infer the solids' congruence by Cavalieri's Principle
. The radii are congruent. The bases are congruent. The altitudes are congruent. The bases are parallel.
2 answers:
I presume the two solids are similar to those in the picture attached.
Cavalieri's principle states that if two solids have equal height and if the cross-sections intersected by planes parallel to the bases and equally distant from them have always the same ratio, then the two volumes will have the same ratio.
Therefore, we can say that:
1) the radii are congruent (bases and cross-sections are congruent circles);
2) the bases are congruent;
3) the altitudes are congruent;
4) the bases are parallel.
Hence, all four statements are TRUE.
Cavalieri's principle states that if two solids have equal height and if the cross-sections intersected by planes parallel to the bases and equally distant from them have always the same ratio, then the two volumes will have the same ratio.
Therefore, we can say that:
1) the radii are congruent (bases and cross-sections are congruent circles);
2) the bases are congruent;
3) the altitudes are congruent;
4) the bases are parallel.
Hence, all four statements are TRUE.
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