A solid brass cone has base radius 7 cm and weighs 5.39 kg. Brass weighs 7 g per ${\text{cm}}^3$. Find the height of the cone, in cm. Take π = 22/7.

Turn the mass into a volume first: 5.39 kg = 5390 g, and at 7 g per ${\text{cm}}^3$ that is $5390/7=770{\text{cm}}^3$. Then $(1/3)(22/7)(49)h=770$, so $(154/3)h=770$ and $h=770\times 3/154=15$ cm. (Using the 5390 g straight as a volume — never dividing by the density — gives 105 cm; leaving out the 1/3 gives 5 cm; dividing by 3π$r^2$ instead of multiplying by 3 gives 1.67 cm.)