Step 1 :We are given the radius of a ball and a formula that relates the radius and the surface area of the ball. The formula is \(r=\sqrt{\frac{S}{12.6}}\).
Step 2 :We can rearrange this formula to solve for \(S\) (the surface area) given \(r\) (the radius). The rearranged formula is \(S = 12.6 * r^2\).
Step 3 :We substitute the given radius of 12.12 cm into this formula to find the surface area. So, \(S = 12.6 * (12.12)^2\).
Step 4 :After calculating, we find that \(S = 1850.8694399999997\).
Step 5 :We round this to the nearest tenth to get the final answer. So, the surface area of the ball is approximately \(\boxed{1850.9}\) square centimeters.