Math CentralQuandaries & Queries


Question from Normand, a teacher:

When a 300 ton train locomotive is built at exact half scale in all dimensions we assumed the weight would be 150 tons. Like a bar of solid steel cut in half would be.
Why does this not work out?
What are we missing here?

Hi Normand,

When you built the scale model you said "at exact half scale in all dimensions" but in your mind you only cut the steel bar in half in one dimension. You need to cut the length, width and height in half so the volume of the scale model is 1/2 × 1/2 × 1/2 = 1/8 times the volume of the locomotive. Since the weight is proportional to the volume the weight should be 1/8 × 300 = 37.5 tons.

I hope this helps,

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