Question

find the mass of a cube of material 1 with a volume of 20 cubic centimeters. what is the density of material 1? what can you conclude about materials 1 and 2? of the graph for is steeper. because the slope

Explanation:

Step1: Recall density - mass - volume formula

The formula for density $
ho$ is $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume.

Step2: Find density of Material 1 from the graph

Let's assume two - point method. If we take two points on the graph of Material 1: $(V_1, m_1)$ and $(V_2, m_2)$. Suppose $(V_1 = 0, m_1=0)$ and $(V_2 = 4, m_2 = 8)$. Then $
ho_1=\frac{m_2 - m_1}{V_2 - V_1}=\frac{8 - 0}{4 - 0}=2\ g/cm^3$.

Step3: Calculate mass of cube of Material 1

Given $V = 20\ cm^3$ and $
ho=2\ g/cm^3$. Using the formula $m=
ho V$, we substitute the values: $m = 2\ g/cm^3\times20\ cm^3=40\ g$.

Step4: Analyze the graph for conclusion

The steeper the slope of the mass - volume graph, the higher the density. Since the slope of the graph of Material 1 is steeper than that of Material 2, Material 1 has a higher density than Material 2.

Answer:

The mass of the cube of Material 1 is 40 grams. The density of Material 1 is $2\ g/cm^3$. The graph of Material 1 is steeper because it has a higher density. We can conclude that Material 1 has a higher density than Material 2.