Chapter 3, Problem 103A

Interpretation Introduction

Interpretation : The mass of a cube of lead that has the same dimensions is to be calculated.

Concept Introduction : The measure of how densely a material is packed together is called density. It is described as the mass per unit volume.

Answer to Problem 103A

The mass of a cube of lead is $510\text{g}$ .

Explanation of Solution

Given information:

The mass of a cube of iron is $\text{355}\text{g}$ .

Iron has a density of $7.87{\text{g/cm}}^3$ .

Lead has a density of $11.3{\text{g/cm}}^3$ .

The connectivity between mass and volume is density. The formula of density is given as:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

To calculate the mass of lead, first, need to find the volume of iron.

The volume of iron can be used as the volume of lead because it has the same dimensions.

Since the density and mass of iron are given, the volume of iron can be found by rearranging the above formula and substituting the values.

  $\begin{array}{c}\text{Volume =}\frac{\text{mass}}{\text{density}}\\ =\frac{355\cancel{\text{g}}}{7.87\cancel{\text{g}}{\text{/cm}}^3}\\ =45.1{\text{cm}}^3\end{array}$

The volume is $45.1{\text{cm}}^3$ .

To calculate the mass of lead, substitute the values in the formula.

  $\begin{array}{c}\text{mass}\text{=}\text{volume}\times \text{density}\\ =45.1\cancel{{\text{cm}}^3}\times 11.3\text{g/}\cancel{{\text{cm}}^3}\\ =510\text{g}\end{array}$

The mass of lead is $510\text{g}$ .