Chapter 2.4, Problem 58SSC

Interpretation Introduction

Interpretation:

The slope of the graph by plotting volume and mass needs to be determined.

Concept introduction:

Density of a sample of matter or an object is equal to the mass of the sample divided by the volume of the sample.

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

Answer to Problem 58SSC

The graph from the data give is as:

The slope of the graph is $3.2{\text{g/cm}}^{\text{3}}$.

Explanation of Solution

Data recorded in the table as:

Density Data
Volume (cm3)	Mass (g)
7.5	24.1
12	38.5
15	48.0
22	70.1

From the data given, the graph will be:

Now, for the determination of the slope, divide the difference of the two points on y-axis by the difference of the two points on x-axis. The two values on the x-axis to be used are $\text{12}{\text{cm}}^{\text{3}}$ and $7.5{\text{cm}}^{\text{3}}$. Two values on the y-axis to be used are 38.5 g and 24.2 g. the slope will be we equal to the mass divided by volume here.

$\begin{array}{c}\text{Slope}=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{38.5-24.1}{12-7.5}\\ =\frac{14.4}{4.5}\\ =3.2\end{array}$

Hence, the slope of the graph will be $3.2{\text{g/cm}}^{\text{3}}$.

Conclusion

The graph from the data give is as:

The slope of the graph is $3.2{\text{g/cm}}^{\text{3}}$.