Explanation

Cavalieri’s Principle says:

If two solids have the same height and the same cross-sectional area at every level, then they have the same volume.

This means:

• Shapes do not have to look the same

• If their slices match, their volumes are equal

Dissection methods involve:

• Cutting a solid into pieces

• Rearranging the pieces

• Showing volume stays the same

These ideas help explain why volume formulas work.

Quiz: Cavalieri’s Principle

1. What must be the same for two solids to have equal volume?

2. Do solids need to look identical for Cavalieri’s Principle to apply?

3. What is a cross section?

4. Does rearranging pieces change volume?

5. Cavalieri’s Principle compares height and what else?

Answer Key

1. Height and cross-sectional area

2. No

3. A slice of a solid

4. No

5. Cross-sectional area