Question

be able to read and interpret data on a line - graph.
mass - volume graph for substance x
density of a fluid

1. read values off of the graph.

a. if the mass is 300 grams, what is the volume?
b. what is the mass if you have 40 cm³ of substance x?

1. determine the density of substance x from the graph.

a. what does the slope of the line represent?
b. calculate the density of substance x using the graph. show all work.

1. use claim, evidence, reasoning to answer the question: what is the density of substance x? use your calculations above as evidence.

claim (one - sentence to answer the question):
evidence (what evidence (data) did you use to answer the question?):
reasoning (how does your evidence answer the question?)

Explanation:

Step1: Read values from graph for 3(a)

Locate 300 grams on mass - axis, then find corresponding volume. From the graph, when mass \(m = 300\) g, volume \(V=30\) \(cm^{3}\).

Step2: Read values from graph for 3(b)

Locate 40 \(cm^{3}\) on volume - axis, then find corresponding mass. From the graph, when \(V = 40\) \(cm^{3}\), mass \(m = 400\) g.

Step3: Define density and slope relationship for 4(a)

Density \(
ho=\frac{m}{V}\). On a mass - volume graph, the slope of the line \(s=\frac{\Delta m}{\Delta V}\). So the slope of the line represents the density of substance X.

Step4: Calculate density for 4(b)

Choose two points on the line, say \((V_1,m_1)=(10,100)\) and \((V_2,m_2)=(20,200)\). Then density \(
ho=\frac{m_2 - m_1}{V_2 - V_1}=\frac{200 - 100}{20 - 10}=\frac{100}{10}=10\) g/\(cm^{3}\).

Step5: Make claim for 5

The density of substance X is 10 g/\(cm^{3}\).

Step6: Provide evidence for 5

We used two points \((10,100)\) and \((20,200)\) on the mass - volume graph. Calculating the slope \(\frac{200 - 100}{20 - 10}=10\) g/\(cm^{3}\), and also from reading values like when \(m = 300\) g, \(V = 30\) \(cm^{3}\) and when \(V=40\) \(cm^{3}\), \(m = 400\) g which also implies \(
ho = 10\) g/\(cm^{3}\).

Step7: Provide reasoning for 5

Since density is defined as mass per unit volume (\(
ho=\frac{m}{V}\)) and the slope of a mass - volume graph gives the ratio \(\frac{\Delta m}{\Delta V}\), the slope value is the density of the substance. Our calculations from different data - points on the graph consistently give a value of 10 g/\(cm^{3}\), so the density of substance X is 10 g/\(cm^{3}\).

Answer:

3(a). 30 \(cm^{3}\)
3(b). 400 g
4(a). The slope of the line represents the density of substance X.
4(b). 10 g/\(cm^{3}\)
5(Claim). The density of substance X is 10 g/\(cm^{3}\).
5(Evidence). Calculations from points on the mass - volume graph such as \(\frac{200 - 100}{20 - 10}=10\) g/\(cm^{3}\), and mass - volume pairs like (300 g, 30 \(cm^{3}\)) and (400 g, 40 \(cm^{3}\)).
5(Reasoning). Density is \(
ho=\frac{m}{V}\) and the slope of mass - volume graph is \(\frac{\Delta m}{\Delta V}\), so slope value gives density. Consistent calculations from graph - data give 10 g/\(cm^{3}\).