As I sit here with a nice bottle of Laphroaig, sipping it neat, as should be done, I’ll offer this tidbit in passing to those who indulge in alcohol that must be cooled to be palatable:
In order for ice to melt, it must absorb, IIRC, 32 joules per gram. This is without any temperature change. To raise that same gram one Celsius degree will only absorb 4.19 joules. So, in order to most effectively cool your drink, the ice must melt. For the sake of simplicity, as well as for keeping the ice away from my drink, let’s use a glass of ice water for a short example.
OK, let’s say you have a pint or so of water, which in the infernal metric system (since that is the one I know the figures for) is 500 mL. We’ll pretend that water has a constant density, since it pretty much does, and call that 500 grams of water. Let’s say that the water is at 20º C. You want it to cool down to 5º C.
At 4.19 J/g for each Celsius degree that you want to lower the water temperature, that means that you need to absorb 62.85 J of heat from the ice. To accomplish that simply from the ice melting, you need 1.96 g of ice. Hmmm, that sounds a bit low, maybe I’m incorrect in my recollections from 10th grade Physics. But you can see what I’m getting at, right?
Anyways, the point is that you will need less ice if it melts quickly, assuming that you want a cold drink, rather than a drink with ice cubes in it. Since the ice melts more quickly as the surface area in contact with the water increases, and less quickly as the temperature differential decreases, you want a shape that will gain surface area as it melts.
Now to switch over to a completely different field of knowledge that I happen to have, namely naval gunfire ballistics. The types of charges used in naval guns (the ones on the ship, personal firearms are never called guns) are classified by whether their surface area increases, decreases, or remains constant as it burns. The hollow cylinder shape is of the “remains constant” category. Shapes that increase in surface area have multiple holes through the center.
I guess it all comes down to what you want to do with your ice. The hollow cylinder shape seems well suited for water, where you want to cool the drink as quickly as possible, and don’t mind at all if it’s “watered down”. The standard cube shape seems better suited for use in cocktails where you don’t mind a little bit of watering down, but not too much, and you don’t necessarily need the drink as cold.
In summation, I’ll suggest two solutions. The first is to stick with drinks, like this fine single malt scotch here, which do not require any cooling to enjoy fully. The second, for those who aren’t as well off as I (not every occupation is as financially rewarding as convenience store clerk, it seems), is to simply down the damn drink more quickly.