In Wagner’s opera Das Rheingold, the goddess Freia is ransomed for a pile of gold just tall enough and wide enough to hide her from sight. Estimate the monetary value of this pile. The density of gold is$\mathbf{19}\mathbf{.}\mathbf{3}\mathbf{}\mathit{g}\mathbf{/}\mathit{c}{\mathit{m}}^{\mathbf{3}}$19.3 g / cm², and take its value to be about $\mathbf{\$}\mathbf{10}$per gram.

Here,

Density of a substance is the ratio of the mass to that of the volume of the substance. Density is a quantity that describe how closely the atoms are packed of the system.

The SI unit of density is . Kg / m³

Here density of gold is given 19.3 g / cm³

Convert the given mass density into dollars per cubic feet.

Let usConvert the given mass density into dollars per cubic feet

Because each conversion factor has a value of $1$they may be squared or cubed without affecting the results. $$\begin{gathered} =19.3\frac{\mathrm{g}}{{\mathrm{cm}}^3}\times \frac{\$10}{1\mathrm{g}}\times {\left(\frac{2.54}{1\mathrm{m}}\right)}^3\times {\left(\frac{12\mathrm{m}}{1\mathrm{ft}}\right)}^3 \\ =5.47\times 106\raisebox{1ex}{$\$$}\!\left/ \!\raisebox{-1ex}{$f{t}^3$}\right. \end{gathered}$$

To calculate the ransom value, multiply the monetary density by Freia's volume (roughly that of a rectangle box $5ft\times 2ft\times 2ft$).

$\begin{array}{rcl}& & 5.48\times {10}^6\frac{\$}{f{t}^3}\times 5ft\times 2ft\times 2ft\\ & =& \${10}^8\end{array}$

Therefor the value of gold will be around $100$million dollars