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

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$1.14 \times 10^{4} k g / m^{3}$

$2.28 \times 10^{4} k g / m^{3}$

$2.14 \times 10^{3} k g / m^{3}$

$1.28 \times 10^{3} k g / m^{3}$

answer is A.

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Detailed Solution

The density of lead is $1.13 \times 10^{4} k g / m^{3}$ , so we should expect our calculated value to be close to this value. The density of water is $1.00 \times 10^{3} k g / m^{3}$ , so we see that lead is about 11 times denser than water, which agrees with our experience that lead sinks.
Density is defined as $ρ = m / V$ . We must convert to SI units in the calculation.
$\begin{array}{l} ρ = (\frac{23.94 g}{2.10 c m^{3}}) (\frac{1 k g}{1000 g}) {(\frac{100 c m}{1 m})}^{3} \\ = (\frac{23.94 g}{2.10 c m^{3}}) (\frac{1 k g}{1000 g}) (\frac{1000 000 c m^{3}}{1 m^{3}}) \\ = 1.14 \times 10^{4} k g / m^{3} \end{array}$