We can use the formula $r=\sqrt{\frac{S}{12.6}}$ to relate a ball's surface area $S$ (in square centimeters) to its radius $r$ (in centimeters). Suppose a ball has a radius of 12,12 centimeters. What is its surface area?

Carry your intermediate computations to at least four decimal places, and round your answer to the nearest tenth.
square centimeters

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.