Math CentralQuandaries & Queries


Subject: centimeters to cubic meters and grams to kilograms
Name: Colleen
Who are you: Student

A box of balls measures 120cm by 20cm by 20cm and weighs 48 g.
One thousand boxes = x cubic meters and weighs x kilograms.
Also, one million boxes = x cubic metes and weighs x kilograms.
One billion boxes = x cubic meters and weighs x kilograms. Solve for x.

Hi Colleen. What a neat question!

I'd start by first converting to cubic meters and kilograms:
120 cm by 20 cm by 20 cm = 120 x 20 x 20 / 1003 = 0.048 m3
48 g = 48 / 1000 = 0.048 kg.

Notice that these two numbers are the same? That means no matter how many boxes you have, you have the same number of kilograms as cubic meters. This is because the "density", which is the mass divided by the volume is 0.048/0.048 = 1 kg/m3.

Hope this helps,
Stephen La Rocque.

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