A $3 \mathrm{~cm}$ diameter copper sphere is to be coated with a $0.5 \mathrm{~mm}$ thick silver layer. For this purpose, we place it in a silver nitrate solution. The current available to us can produce $11.11 \mathrm{~cm}^{3}$ of hydrogen. For how long does this current need to work? The equivalent ratio of hydrogen to silver is 1:108. The density of silver is 10.5.
The volume of the silver shell is the difference in volume between spheres with diameters of $3.1 \mathrm{~cm}$ and $3 \mathrm{~cm}$, that is, $\frac{1}{6} \pi\left(3.1^{3}-3^{3}\right)$.

The necessary mass of silver: $\frac{1}{6} \pi\left(3.1^{3}-3^{3}\right) 10.5=15.344 \mathrm{g}$.

The available current produces

$$
11.11 \times 0.001293 \times 0.0695=0.000998 \mathrm{g}
$$

of hydrogen per minute. According to Faraday's law, the same current can extract

$$
0.000998 \times 108=0.10778 \mathrm{g}
$$

of silver. Therefore, the current needs to run for

$$
\frac{15.344}{0.10778}=142 \text{ minutes}
$$

to achieve the goal specified in the problem.

Kozma István (Bolyai g. VIII. o. Bp. V.)