Height From the Surface

If the surface area and the radius are known, the height is fixed. The height appears only in the curved side's term, so the equation is linear in h.

This cylinder has radius 3 and surface area 48π. The rule says $48\cdot \pi = 2\cdot \pi\cdot {3}^{2}+2\cdot \pi\cdot 3\cdot h$. Divide everything by π: $48 = 18+6\cdot h$. Then $30 = 6\cdot h$ and $h = 5$.

As with volumes, the board writes the equation already divided by π. Work out the ends' term first, then subtract it.