21 - University Physics with Modern Physics

Question

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 19.3 g/cm³, and take its value to be about $10 per gram.

Step-by-Step Solution

Answer

The monetary value of the pile is  $69.68 million dollar.

Mass of pile

The dimension of the pile is $18 in\times 18 in\times 68 in$ .

 The volume of pile in cm³ will be,

$$\begin{gathered} V=18 in\times 18 in\times 68 in \\ V=22032 i{n}^3\times {\left(\frac{2.54 cm}{1 in}\right)}^3 \\ V=361039.794 c{m}^3 \end{gathered}$$ 

 

Since the density of gold is $\rho =19.3 g/c{m}^3$ .

The mass of gold can be calculated as,

 $$\begin{gathered} m=\rho V \\ m=\left(19.3 g/c{m}^3\right)\left(361039.794 c{m}^3\right) \\ m=6968068.025 g \end{gathered}$$

The calculation for monetary value

The price per gram is  $c=\$10/g$.

 

The price of the pile can be calculated as,

  $$\begin{gathered} C=mc \\ C=\left(6968068.025 g\right)\left(\$10/g\right) \\ C=\left(6968068.025 g\right)\times \frac{1 million}{{10}^6} \\ C=69.68 million dollar \end{gathered}$$ 

Thus, the monetary value of the pile is $69.68 million dollar.