Discussion
Alumina has a density of about 3.9 and boron carbide about 2.5 grams per cubic centimetre. For the same volume, what proportion of the alumina mass does the boron carbide represent?
Answer: B
Correct answer: about 64 per cent
For the same volume the mass ratio is the density ratio: \[ \frac{2.5}{3.9} = 0.641, \] so about 64 per cent. Inverting it gives the 156 per cent offered. This is the calculation behind boron carbide’s use in armour and neutron shielding - comparable hardness at roughly two thirds of the weight is decisive where the material must be carried.
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