The dog runs from the North side to the South side of the tree (semi-circle) with the cord to its full length at all times.
The dog runs approximately 30 feet.
Target question: what was the approximate length of the nylon cord, in feet?
$$Circumference\ of\ a\ fall\ circle=2\pi r$$
$$Circumference\ of\ a\ semi\ circle=\frac{2\pi r}{2}=\pi r$$
Since the dog covered 30 feet
$$\pi r=30;\ \ Take\ \pi\ to\ be\ 3.142$$
So, 3.142r = 30
$$r=\frac{30}{3.142}=9.55\approx10feet$$
Therefore, option D is the correct answer