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First of all, the question needs to be adjusted. Say the last number is 18' (eighteen foot).
The problem is to use the density of granite correctly. From wikipedia, we find that the density d is somewhere between 2.65 g/m^3 and 2.75 g/m^3. So let's take d = 2.70 g/m^3, the average.
Now, since 1 in = 2.54 cm and 1 ft = 12 in, we find that
1 cubic ft = 12^3 cubic in = (2.54 * 12)^3 cm^3 = 28.3 10^3 cm^3
The mass (m) equals the volume (V) times the density (d), so
m = V*d
= 216 * 28.3 * 10^3 * 2.70
= 1.65 10^7 g
= 1.65 10^4 kg
1 ton = 907 kg, so
m = 1.65 10^4/907 tons = 18.2 tons,
which is about 1% deviated from 18 tons.
Since we deviated the density for a max of about 2%, we could make a rule of thumb:
A 4' x 3' x n' piece of granite weighs n tons. Nice.
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∙ 11y ago
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