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Another Round of Ice?

I go to the ends of the Internet earth to find interesting applications of mathematics. The "find" for this week is the spherical ice cube!

Why spherical? Think for a minute before continuing to read, as the reason involves only some elementary mathematics.

A spherical ice cube has a lower surface-area-to-volume ratio than a typical ice cube. And, this reduced surface size implies that the ice will melt at a slower rate...and thus keep whatever you are drinking from getting "watery" to fast.

Problem: Suppose you have a ice cube that is 1"x1"x1". First, determine the radius of a spherical ice cube with the same volume. Second, determine the surface-area-to-volume ratio for the two cubes. Third, is this ratio constant regardless of the dimensions of the original cube of ice?

So, the new question is...how does one create a spherical ice cube? I am assuming that you do not want to sit there and slowly shave a cube into a sphere!

A Japanese company has created a mold that produces a perfect ice sphere. A chunk of ice is placed in the metal press; as the ice chunk melts, the press closes around the ice and forms a ball. The mold comes in multiple sizes (55 mm, 65mm, 70 mm, and 80 mm) and makes 30-40 ice spheres in an hour.

Or, you can buy spherical ice cube trays for about $15!

Source: Wired, July 2009, p. 55