Surface area of a sphere equals the curved surface area of a cylinder. Cylinder height (h) = 12 cm, diameter (d) = 12 cm.

Since the cylinder's diameter is 12 cm, its radius R is 6 cm. Using the formula $4\pi r^2 = 2\pi R h$, we have $4r^2 = 2(6)(12) = 144$. Thus $r^2 = 36$ and $r = 6$.

Many students confuse radius and diameter, or forget that the curved surface area of a cylinder is $2\pi Rh$ whereas the surface area of a sphere is $4\pi r^2$.

This concept of equating surface areas or volumes is frequently used in 3D geometry transformation problems (e.g., melting a sphere to cast a cylinder).