In the traditional story of Archimedes and the gold crown, he proved that the crown was not pure gold by measuring its density. Suppose the crown...

The
"eureka" moment for Archimedes was to realize that the volume of an irregularly shaped
object can be determined by the volume of water it displaces when submerged.  He already knew
that the density of a pure substance would always be the same regardless of its volume as
density is what we would now call and intrinsic property.

The relationship
between density, mass, and volume is given by the equation  d = m/V  where 'd' is the density,
'm' is the measured mass, and 'V' is the displaced volume (or volume of the object in
question).

In the case of this problem we want to work the problems slightly
backwards.  We already know the density of pure gold and the mass of the sample.  What we want
to know is what the displaced volume will be.  We need simply to do "cross multiplication
and division" to solve the density equation for the volume:

V =
m/d

With this in hand, we can how substitute the given quantities and
calculate the volume:

V = 6.00X10^2g/19.3g/cm^3

V =
31.0808 cm^3 which needs to be rounded to three signficant digits.  So we would say that the
displaced volume is 31.1 cm^3