# Tutoring high school math, unit conversions are often visited. The math tutor discusses the conversion of engine displacements.

Back when I was a kid, I had a 50cc (**cc**:**c**ubic **c**entimetre, also written as cm^{3}) minibike. My friends soon got an 80cc one. That’s when the numbers “50cc” or “80cc” became important to me: their 80cc bike was not just a minibike. It could go 60mph (we still talked in miles back then); it always had more power than you needed. That was the difference between a “50” and an “80”.

Through many moves, new friends who didn’t ride motorbikes, jobs, then university, I became completely removed from the motorcycle culture. In high school I heard about old muscle cars; a few of my friends even had them. The numbers were “289”, “350”,or “400”. I was told those numbers also described engine size, but they meant cubic inches rather than cubic centimetres. At the same time, more of my friends had smaller cars whose engines were measured in litres: 1.6L, 2.6L, or 3.8L, for instance.

The inevitable question in such a context: what is a 350 cubic inch engine in litres? Or in cubic cm? How can we arrive at a common unit so as to compare the sizes of those engines?

We can do so with the help of this diagram:

It’s a fact that, for a box structure, the volume (aka, displacement) is given by

Therefore, the volume of the cubic inch pictured above, in cubic centimetres, would be

Therefore, rounded to the nearest hundredth,

It follows that a 350inch^{3} engine is , or 5736.5cc’s, if you prefer that way of saying it.

Another fact is that

Furthermore,

Therefore, your 5736.5cc engine is also 5736.5mL, which is 5.7365L.

My old minibike of 50cc? Well, I guess it was . For its size, though, it really got around:)

We’ve hit a cool, damp stretch of days here, but we needed it. Wherever you are, hope your summer is turning out well, too.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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