Rounding a 10-meters long rope to form a circle will give you a circle whose circumference is 10 meters. In every circle, the following formula links radius and circumference together:
[tex] C = 2\pi r \iff r = \dfrac{C}{2\pi} [/tex]
So, in your case, the radius will be
[tex] r = \dfrac{10}{2\pi} = \dfrac{5}{\pi} \approx 1.591549\ldots [/tex]
which we can best approximate as 1.59
