Question

A penny has a mass of 3.0 g, a diameter of 1.9 cm, and a thickness of 0.15 cm. what is the density of the metal of which it is made?

Answer 1

To calculate the density of an object, we must divide its mass by its volume.
For the case of the given penny, since it is cylindrical in form, then to solve for the volume, we have
`V = \pi r^(2)`. Since the penny has a diameter of 1.9 cm, then it has radius of 1.9/2 = 0.95 cm.
Thus, its volume is
`V = (3.14)(0.95)^(2)= 2.84 cm^(3)`
Now to get the density, we have

`density = (3.0 g)/(2.84 cm^(3))`
Therefore, the penny's density is
`1.05 cm^(3)`.

Answer 2

A penny has m = 3.0 g.
Diameter: d = 1.9 cm
r = d / 2 = 1.9 / 2 = 0.95 cm
Thickness = 0.15 cm. h = 0.15 cm.
The volume of a penny is: V = r² · π · h
V = 0.95² · 3.14 · 0.15
V = 0.425 cm³
Density = m / V = 3.0 g / 0.425 cm³ = 7.0588 g/cm³
Answer: The density of a coin is 7.0588 g/cm³ and the closest value from a table of materials is for cast Iron.