Answer
The average density of this piece is $7.02\times 10^3~kg/m^3$. Since the actual density of gold is $19.3\times 10^3~kg/m^3$, it seems clear that we were cheated.
Work Step by Step
We can find the volume of the metal.
$V = (5.0\times 10^{-3}~m)(15.0\times 10^{-3}~m)(30.0\times 10^{-3}~m)$
$V = 2.25\times 10^{-6}~m^3$
We can find the average density of the metal.
$\rho = \frac{M}{V}$
$\rho = \frac{0.0158~kg}{2.25\times 10^{-6}~m^3}$
$\rho = 7.02\times 10^3~kg/m^3$
The average density of this piece is $7.02\times 10^3~kg/m^3$. Since the actual density of gold is $19.3\times 10^3~kg/m^3$, it seems clear that we were cheated.
