The optimum shape of a riser is spherical to ensure that it cools more slowly than the casting it feeds. Spherically shaped risers, however, are difficult to cast.

(1) Sketch the shape of a blind riser that is easy to "old but also has the smallest possible surface-area-to volume ratio. (2) Compare the solidification time of the riser in part (1) to that of a riser shaped like a right circular cylinder. Assume that the volume of each riser is the same, and that for each the height is equal to the diameter.