Chapter 18, Problem 24A

Which has more volume—a kilogram of lead or a kilogram of aluminum?

To determine

To identify: The quantity that has more volume.

Answer to Problem 24A

The volume of 1 kilogram aluminium is greater than volume of one kilogram lead.

Explanation of Solution

Given:

Quantity of Lead = 1kg

Quantity of Aluminium = 1kg

Formula used:

Density of a material is defined as ratio of mass per unit volume of the material.

Mathematically, it can be expressed as

Density $=\frac{\text{Mass}}{\text{Volume}}$

Calculation:

The volume of the $1\text{kg}$ lead of density ${\rho }_{\text{L}}=11.3\text{g}/{\text{cm}}^3$ is,

  $\begin{array}{c}V=\frac{m}{\rho }\\ =\frac{(1\text{kg})\left(\frac{1000\text{g}}{1\text{kg}}\right)}{11.3\text{g}/{\text{cm}}^3}\\ =88.49{\text{cm}}^3\end{array}$

The volume of the $1\text{kg}$ aluminum of density ${\rho }_{\text{Al}}=2.7\text{g}/{\text{cm}}^3$ is,

  $\begin{array}{c}{V}_{Al}=\frac{m}{\rho }\\ =\frac{(1\text{kg})\left(\frac{1000\text{g}}{1\text{kg}}\right)}{2.7\text{g}/{\text{cm}}^3}\\ =370.37{\text{cm}}^3\end{array}$

Thus, the volume of aluminium is greater than the lead.

Conclusion:

Therefore, the volume of 1 kilogram Aluminium is greater than volume of one kilogram Lead.