To solve this problem, we need to first calculate the surface area of the Hoberman sphere when it is fully closed, and then when it is fully expanded.
The surface area of a sphere is given by the formula A = 4 * pi * r^2, where r is the radius of the sphere. The diameter of the sphere is equal to 2 times the radius, so we can rewrite the formula as A = 4 * pi * (d/2)^2.
Plugging in the values from the problem, we get:
When fully closed: A = 4 * pi * (5.9/2)^2 = 4 * pi * 2.95^2 = 54.77 in^2
When fully expanded: A = 4 * pi * (30.1/2)^2 = 4 * pi * 15.05^2 = 1413.24 in^2
The difference in surface area is 1413.24 in^2 - 54.77 in^2 = 1358.47 in^2.
Rounded to three decimal places, the difference in surface area is 1358.47 in^2 = 1358.470 in^2.
So the difference in surface area of a Hoberman sphere from when it is fully closed to when it is fully expanded is 1358.470 in^2.