## 251. Math Puzzle $4 / 86$

The "Golden Rider" in Dresden almost magically draws the gaze of passersby, living up to its name. During the last restoration, it was overlaid with 140 g of gold leaf, which has a specific density of $19.3 \mathrm{~g} / \mathrm{cm}^{3}$.

How thick is the average gold coating if the monument has a surface area to be coated of $40 \mathrm{~m}^{2}$?
The thickness of the gold coating on the "Golden Rider" is $x$, with a density $\rho$. The mass of the layer is given by:

$$
m=140 \mathrm{~g}=A \cdot \rho \cdot x
$$

The area and density were given: $A=40 \cdot 10^{4} \mathrm{~cm}^{3}$ and $\rho=19.3 \mathrm{~g} / \mathrm{cm}^{3}$. Substituting the values, we get

$$
x=0.181 \cdot 10^{-4} \mathrm{~cm}=0.18 \mu \mathrm{m}
$$

The monument is coated with a $0.18 \mu \mathrm{m}$ thick layer of gold.