Question

Two pillars have been delivered for the support of a shade structure in the backyard. They are both ten feet tall and the cross sections of each pillar have the same area. Explain how you know these pillars have the same volume without knowing whether the pillars are the same shape.

Answer 1

Cavalieri's Principle

If in two solids of equal altitude, the sections made by planes parallel to and at the same distance from their respective bases are always equal, then the volumes of the two solids are equal.

Answer 2

Answer:

These pillars have the same volume according to Cavalieri's Principle

Step-by-step explanation:

The given two pillars are ten feet tall and the cross sections of each pillar have the same area.

These pillars have the same volume according to Cavalieri's Principle.

This principle states that if two solids have the same height, an their cross sections reveal the same area, then they have equal volumes.

The given two pillars have equal height and the cross sections have same area, so they are true to this principle, and thus have same volumes.