## I want to make a Chocolate Chip so Big…..

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Last night at dinner, out of the blue, out 8-year old announced, “I want to make a chocolate chip so big that if it was 6 ft tall, a person would be a millimeter.” We all pondered the Giant Chocolate Chip, and then he asked if it would cover the United States. I said I didn’t think so, and he asked if it would cover any state. “Maybe Rhode Island,” was my reply.

Or maybe not. Curious about just how big that chocolate chip would have to be, I bought some “research supplies” and measured them. It turns out that a chocolate chip is 8 millimeters tall (with a tiny bit of variation, but not enough for me to measure effectively). According to the bastion of truth, the average height of an adult male in the US is 175.8 centimeters (just over 5′9″) and the average height of an adult female in the US is 162.0 centimeters (almost 5′4″). Therefore I declare the average height of an adult in the United States to be 168.9 cm. This gives us:

$\frac{\mbox{Giant Chocolate Chip}}{\mbox{person (168.9 cm)}} = \frac{\mbox{6 feet}}{\mbox{1 mm}}$

That’s a lot of different units there. Let’s convert to centimeters. The millimeter is just 0.1 cm, and we know that 6 feet is 6·12·2.54 cm since there are 12 inches in a foot and 2.54 centimeters in an inch. Speaking of which, did you know that there are EXACTLY 2.54 centimeters in an inch? That even though inches are way older than centimeters, that inches have been redefined to be exactly 2.54 centimeters? Apparently this happened in 1958, but I only found out about it last month.

So anyway, we know that 6 feet is 182.88 cm, which gives us:

$\frac{\mbox{Giant Chocolate Chip}}{\mbox{person (168.9 cm)}} = \frac{\mbox{182.88 cm}}{\mbox{0.1 cm}}$

This means that the height of the Giant Chocolate Chip is (168.9)·(1828.8)=308884.3 centimeters. That’s about 3.1 kilometers, or about 1.9 miles. That’s a BIG chocolate chip.

But not big enough to cover Rhode Island. The diameter of a regular chocolate chip is 1 centimeter, which is really cool if you are looking for a mental way to envision centimeters. That means that the diameter of the giant chocolate chip is about 2.4 miles, giving an area of 3.76 square miles. And Rhode Island is actually 1,545 square miles, so you’d need 410 giant chocolate chips to match the area.

But this got me thinking — there’s a lot of chocolate in that humongous chocolate chip. What if we melted it down and spread it out over Rhode Island? How deep would it be? Thinking of a chocolate chip as a cone (which ignores the little swirl on the top), the volume of chocolate is (1/3)·(area of the base)·(height), which for our Godzilla chip is about 2.4 cubic miles. And if it was really hot and the giant chocolate chip melted, it would cover Rhode Island to a depth of 99 inches.

Yummmmmmm!