jmc

Consider a cross-section of this problem in which a circle lies with its center somewhere above a line. A line segment of $8$ cm can be drawn from the line to the bottom of the ball. Denote the distance between the center of the circle and the line as $x$. We can construct a right triangle by dragging the center of the circle to the intersection of the circle and the line. We then have the equation $x^2+(12{)}^2=(x+8{)}^2$, $x^2+144=x^2+16x+64$. Solving, the answer is $\boxed{13}$.