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To solve this problem:

1. Calculate the volume of water displaced:

The surface area of the swimming bath is .

The water rises by 1 cm (or 0.01 m), so the total volume of displaced water is:

$$

\text{Total displaced water} = 360 , \text{m}^2 \times 0.01 , \text{m} = 3.6 , \text{m}^3 $$

2. Find how many men are in the pool: Each man displaces 0.1 m³ of water.

The number of men can be calculated by dividing the total displaced water by the volume displaced by each man:

\text{Number of men} = \frac{3.6 , \text{m}^3}{0.1 , \text{m}^3} = 36 , \text{men}

Thus, there are 36 men in the bath.