A solid plastic sphere with a radius of 6 cm is melted and recast into a right circular cylindrical rod with a radius of 3 cm. What is the ratio of the total surface area of the cylindrical rod to that of the original sphere?

Volume of sphere = (4/3) * pi * 6^3 = 288 * pi. Volume of cylinder = pi * 3^2 * h = 9 * pi * h. Equating volumes, 9 * pi * h = 288 * pi, so h = 32. Surface area of sphere = 4 * pi * 6^2 = 144 * pi. Surface area of cylinder = 2 * pi * 3^2 + 2 * pi * 3 * 32 = 18 * pi + 192 * pi = 210 * pi. The ratio is 210 : 144, which simplifies to 35 : 24.