Cavalieri's Principle and Density

Front

What is density?

Back

Density is the mass of an object divided by its volume, typically expressed in grams per cubic centimeter (g/cm³).

Front

How do you calculate density?

Back

Density = Mass / Volume.

Front

What is the formula for calculating the mass of an object if its density and volume are known?

Back

Mass = Density × Volume.

Front

If an object has a mass of 10g and a volume of 2cm³, what is its density?

Back

5 g/cm³.

Front

What is Cavalieri's Principle?

Back

Cavalieri's Principle states that if two solids have the same height and the same cross-sectional area at every level, they have the same volume.

Front

True or False: Two objects with different shapes can have the same volume if they have the same height and cross-sectional area.

Back

True.

Front

What is the unit of measurement for density?

Back

The unit of measurement for density is grams per cubic centimeter (g/cm³).

Front

If a diamond has a density of 3.5 g/cm³ and a volume of 1 cm³, what is its mass?

Back

3.5 g.

Front

What is the relationship between mass, volume, and density?

Back

Mass is directly proportional to density and volume; as one increases, the others may change depending on the context.

Front

If an object has a density of 2 g/cm³ and a volume of 4 cm³, what is its mass?

Back

8 g.