Calculate the circumference of the cylinder.

The radius of the cylinder is $r = 25$ cm.
The formula for the circumference of a circle is $C = 2\pi r$.
Using $\pi = 3.14$:

$$C = 2 \times 3.14 \times 25 \text{ cm}$$ $$C = 50 \times 3.14 \text{ cm}$$ $$C = 157 \text{ cm}$$

The rope is wound 50 times around the cylinder. So, the total length is the circumference multiplied by the number of turns.

$$\text{Total length} = C \times \text{Number of turns}$$ $$\text{Total length} = 157 \text{ cm} \times 50$$ $$\text{Total length} = 7850 \text{ cm}$$

The total length of the rope is $\text{7850 cm}$.