Problem

\(\text{One}~\text{stack}~\text{of}~\text{identical}~\text{coins}\) is straight up, and another stack of the same coins is shifted sideways so it leans. The \(\text{two}~\text{stacks}\) have the same height, and at every height the horizontal cross-sectional area is the same. Using \(\text{Cavalieri}'s~\text{principle}\), what can you conclude about their volumes?

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The leaning stack has greater volume because it spreads sideways, so it takes up more space.

You cannot conclude the volumes are equal, because Cavalieri’s principle only works when the two solids have the same overall shape.

The straight stack has greater volume because stacking coins directly above each other makes the solid more compact.

Using Cavalieri’s principle, the two stacks have equal volumes because they have the same height and the same horizontal cross-sectional area at every height.

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