A penny has a mass of 2.50 g, a diameter of 19.55 mm, and a thickness of 1.55 mm. Calculate the density of the material from which the penny is made.

Density = (mass) divided by (volume)

We know the mass (2.5 g). We need to find the volume.

The penny is a very short cylinder.

The volume of a cylinder is (π · radius² · height).

The penny's radius is 1/2 of its diameter = 9.775 mm.

The 'height' of the cylinder is the penny's thickness = 1.55 mm.

Volume = (π) (9.775 mm) ² (1.55 mm)

= (π) (95.55 mm²) (1.55 mm)

= (π) (148.1 mm³)

= 465.3 mm³

We know the volume now. So we could state the density of the penny,

but nobody will understand what we have. Here it is:

mass/volume = 2.5 g / 465.3 mm³ = 0.0054 g/mm³.

Nobody every talks about density in units of ' gram / (millimeter) ³ '.

It's always ' gram / (centimeter) ³ '.

So we have to convert our number for the volume.

(0.0054 g/mm³) x (10 mm / cm) ³

= (0.0054 x 1,000) g/cm³

= 5.37 g/cm³.

This isn't actually very close to what the US mint says for the density

of a penny, but it's in a much better ball park than 0.0054 was.