Answer
The height of the cube would be 10.8 cm
Work Step by Step
We can find the mass of the cube.
$M = \frac{\$1,000,000}{\$1282/troy~ounce} = 780~troy~ounces$
We can convert the mass to units of kilograms.
$M = (780~troy~ounces)(\frac{31.1035~g}{1.0000~troy~ounces})(\frac{1~kg}{1000~g})$
$M = 24.26~kg$
We can find the volume of the cube.
$V = \frac{M}{\rho}$
$V = \frac{24.26~kg}{19.3\times 10^3~kg/m^3}$
$V = 1.257\times 10^{-3}~m^3$
We can find the length of each side of the cube.
$L = (V)^{1/3}$
$L = (1.257\times 10^{-3}~m^3)^{1/3}$
$L = 0.108~m = 10.8~cm$
The height of the cube would be 10.8 cm
