At tonight's Oscars we'll no doubt see some familiar faces winning that coveted gold statuette. It's no secret that these sparkling little men aren't 100% gold--they're only coated in 24-carat gold--so that makes it harder to figure out how much gold they actually contain. Luckily math comes to the rescue.
Let's start with some data. The trophy's official height and weight are: 13.5 inches, and 8.5 pounds, respectively. So, it's basically a newborn baby (well, except that it's coated in gold, has a fit physique, and comes with a sword). This means that all we need to do is find the surface area of this golden baby. There are several formulas for doing so, but one developed by G.B. Haycock in 1978 has been shown to give good results:
The output of this formula is in square meters, and "W" is the weight in kilograms and "H" the height in centimeters, so a little number-crunching is needed (I've put the details here). The result? Our golden boy has a surface area of about...
0.2 square meters, or 2.2 square feet.
I think those numbers are hard to visualize, so here's some help. Stretch out your arm. Now bend your forearm to create an "L." The length of the forearm from the elbow to the tip of your middle finger is approximately 18 inches, or 1.5 feet. (This unit of length was widely used in ancient times; it's called a cubit.) And, since the square of 1.5 is 2.25, if you touch your elbow with the fingers on your other hand, the square you create (see below) has roughly the area of an Oscar statuette's gold-coated surface.
Thus far we've only estimated the surface area of the statuette. If we knew the thickness of the gold coating we could estimate the volume of gold in an Oscar trophy. But, since the coating is probably a very thin layer, we'll just stop here. (Edit: As a reader pointed out, average coatings are 15 millionths of an inch thick. Using this and the 2.2 square feet calculation gives about 0.0047 cubic inches of gold. That's about 1/500-th the volume of a golf ball.)
So there you have it. Today's winners will be taking home armfuls of gold. For the rest of us, here's a recipe for Oscar cookies. Enjoy the show!