Question

A solid piece of lead has a mass of $23.94g$ and a volume of $2.10c{m}^3$. From these data, calculate the density of lead in SI units (kilograms per cubic meter).

Answer 1

The density of lead is $1.13\ast {10}^{4}kg/m^3$, so we should expect our calculated value to be close to this value. The density of water is $1.00\ast {10}^{3}kg/m^3$, so we see that lead is about $11$ times denser than water, which agrees with our experience that lead sinks.

Density is defined as $\rho =m/V$. We must convert to SI units in the calculation.

$\rho =\left(\frac{23.94g}{2.10c{m}^3}\right)\left(\frac{1kg}{1000g}\right){\left(\frac{100cm}{1m}\right)}^3$

$=\left(\frac{23.94g}{2.10c{m}^3}\right)\left(\frac{1kg}{1000g}\right)\left(\frac{1000000c{m}^3}{1m^3}\right)$

$=1.14\ast {10}^{4}kg/m^3$

Observe how we set up the unit conversion fractions to divide out the units of grams and cubic centimeters, and to make the answer come out in kilograms per cubic meter. At one step in the calculation, we note that one million cubic centimeters make one cubic meter. Our result is indeed close to the expected value. Since the last reported significant digit is not certain, the difference from the tabulated values is possibly due to measurement uncertainty and does not indicate a discrepancy.