All courses Math II · G-GMD.1 37 of 73

Explain circumference, area, and volume formulas using informal arguments such as dissection, Cavalieri, and limits.

Use Cavalieri's principle to compare volumes

Problem

Using Cavalieri's principle, what can you conclude about the volumes of two prisms with equal height and equal cross-sectional area at every level?

Geometric source configuration showing only the supplied dimensions and construction.

Your answer

Show answer choicesAnswer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.

A By Cavalieri’s principle, the two prisms cannot be compared unless their base areas are equal, not just their cross-sections at every level. B By Cavalieri’s principle, the two prisms must have the same volume because they have equal height and equal cross-sectional area at every level. C By Cavalieri’s principle, the two prisms must have the same volume only if they also have the same overall shape. D By Cavalieri’s principle, the two prisms may still have different volumes because equal slices at each level do not determine the whole solid.

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Use Cavalieri's principle to compare volumes

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Hint

Solution walkthrough

List Cavalieri's two hypotheses

State why the principle applies

Apply the implication

Interpret the result

Another way

Common mistake