The rope of a crane and the safety factor

A crane maker offers ropes for loads from half a tonne to ten tonnes. The steel breaks at $4.2 \times 10^{8}\ \text{Pa}$ and the rule is a safety factor of $6$. You will make the program find the rope radius each load needs, and the largest load a rope of radius $1.5\ \text{cm}$ may lift.

The idea. The rope must be able to hold the safety factor times the weight: $\sigma_{\text{break}}\pi r^2 = s\,mg$. So $r = \sqrt{\dfrac{s\,mg}{\pi\sigma_{\text{break}}}}$.

Your tasks.

1. Work out the force each rope must be able to hold before breaking (the design force).
2. Work out the radius each load needs, in metres.
3. Find the largest load (in kg) that a rope of radius $1.5\ \text{cm}$ may lift.