Answer:
First some theory we need to solve this problem.
For a circle of radius R, the perimeter is:
P = 2*pi*R
where pi = 3.14
If we have a section of this circle, defined by an angle θ, the length of this arc will be:
A = (θ/360°)*2*pi*R
In the case of the problem, the total distance that the child travels is equal to the length of an arc of 310° in a circle of radius r = 6ft.
Using the above formula, we know that the length of this arc is:
A = (310°/360°)*2*3.14*(6ft) = 32.4 ft