#### Answer

$1930~cm^3$ of water has the same mass as $100~cm^3$ of gold.

#### Work Step by Step

We can find the mass $M$ of $100~cm^3$ of gold as:
$M = \rho~V$
$M = (19.3\times 10^3~kg/m^3)(100\times 10^{-6}~m^3)$
$M = 1.93~kg$
We then find the volume of this mass of water;
$V = \frac{M}{\rho}$
$V = \frac{1.93~kg}{1.00\times 10^3~kg/m^3}$
$V = 1.93\times 10^{-3}~m^3$
$V = (1.93\times 10^{-3}~m^3)(\frac{1~cm^3}{10^{-6}~m^3})$
$V = 1930~cm^3$
$1930~cm^3$ of water has the same mass as $100~cm^3$ of gold.