Chapter 5, Problem 100A

Interpretation Introduction

Interpretation:

The mass of the gold in kg is to be determined.

Concept Introduction :

The relation between mass, volume, and density is given as,

  $\text{mass = volume}\times \text{density}$

Answer to Problem 100A

  $0.116\text{kg}$

Explanation of Solution

The density of gold is $19.3{\text{g/cm}}^3$ and the length of each edge is 2 cm.

Calculate the volume of gold as,

  $\begin{array}{c}\text{volume = 2 cm }\times \text{2 cm }\times \text{2 cm}\\ \text{= 6}{\text{cm}}^3\end{array}$

Substitute $\text{6}{\text{cm}}^3$ for volume and $19.3{\text{g/cm}}^3$ for density in the above formula.

  $\begin{array}{c}\text{mass = 6}{\text{cm}}^3\times 19.3{\text{g/cm}}^3\\ =115.8\text{g}\end{array}$

Now in kg,

  $1\text{kg = 1}\times {\text{10}}^3\text{g}$

So,

  $\begin{array}{c}115.8\text{g = }115.8\text{g }\times \frac{1\text{kg}}{\text{1}\times {\text{10}}^3\text{g}}\\ =0.116\text{kg}\end{array}$

Conclusion:

The mass of the gold in kg is $0.116\text{kg}\text{.}$