Question

The mass of a cube of iron is 411 g. Iron has a density of 7.87 g/cm3. What is the mass of a cube of lead that has the same dimensions?

Answer 1

The mass of a cube of iron is $411\,\mathrm{g}$. Iron has a density of $7.87\,\mathrm{g/cm^3}$. What is the mass of a cube of lead that has the same dimensions?

Lead density = $2.6\,\mathrm{g/cm^3}$

$$\rho = \frac{m}{V} \Rightarrow V = \frac{m}{\rho}$$ $$V_{iron} = V_{Lead}$$ $$\frac{m_{iron}}{\rho_{iron}} = \frac{m_{Lead}}{\rho_{Lead}} \Rightarrow m_{Lead} = \frac{m_{iron} \cdot \rho_{Lead}}{\rho_{iron}}$$ $$m_{Lead} = \frac{411 \cdot 2.6}{7.87} = 135.78\,\mathrm{g}$$ $$m_{Lead} = 135.78\,\mathrm{g}$$