Tag Archives: surface area

Exothermic fauna: A surface area poem

Two animals

Are both close to a cube

In shape.

The height of the first animal

Is 4 cm

The height of the second animal

Is 6 cm

Which animal

Would experience the greater

Amount

Of heat loss?

Explain.

Thanks to Cathy Yenca and Chris Robinson for the find, whose source is evidently a 2007 U.S. textbook.

mhampton‘s reformulation of my poem (in the comments below) led to some fun over on Twitter, which I collected on Storify.

More junk food math

You’ve seen the billboards for these, right?

Basically, they’re mini McNuggets.

McNuggets have a lot of fat. Most of it (as with all fried foods with the possible exception of cheese curds) is in the outer coating.

So what happens when we shrink the McNugget?

We could model the chicken by volume and the outer coating by surface area. In this case, shrinking the McNugget by a factor 1/2 would yield a doubling of the ratio of coating to chicken. As a result we predict a substantial increase in fat as a percentage of weight.

But that’s a crude model-the coating isn’t infinitely thin.

A more realistic model might treat the coating as having a thickness, and thus a volume. When we shrink the McNugget to make a McBite, do we shrink the thickness of the coating proportionately? This seems unlikely. But even if we do, the ratio of coating to chicken increases.

More likely is that the coating is of constant thickness. In other words, McBites are probably smaller chicken bits covered with the same coating as McNuggets. Once again, we increase the ratio of coating to chicken, and we predict a substantial increase in fat as a percentage of weight.

Heading over to McDonald’s online Nutrition Information, we learn that McNuggets have about 12 grams of fat for a 65 gram serving. That’s about 18% fat by weight. This figure is consistent across serving sizes.

Mc Bites? 19 grams of fat for an 85 gram serving. That’s about 22% fat by weight. Also consistent across serving sizes.

How different is 22% fat from 18% fat, you ask? Very different. They’re both bad news, but 22% fat is (coincidentally) 22% more fat than 18% is. So take a serving of McNuggets, which has a lot of fat. And put almost a quarter more fat in. That’s McBites. Oh, and also increase the portion size from 97 grams (6 piece McNuggets) to 128 grams (Regular size McBites).

Middle school math will get you far, kids.

Now if we can get an estimate of the McNugget to McBite scale factor, we can set up a system of equations and figure out just how much of that fat is in the coating.