CP DATA ANALYSIS LAB

USING A GRAPH TO FIND AREA (MEASUREMENT)

Modern technology makes it possible for paper and cardboard mills to produce products of extremely uniform thickness. Many of these paper products are used in your everyday life. For example, notebook paper, cereal boxes, or tissues. In this activity, you will use samples of ordinary cardstock paper with uniform thickness for the purpose of learning to use a graph for interpolation, or determining an unknown value that lies between two or more known values. Since the thickness of the cardstock is constant, you can measure the mass and area of rectangular samples and graph the data to find a relationship between mass and area (mass/area).

Using the graph, you will then be able to find the unknown area of an irregularly shaped sample.

OBJECTIVES:

Measure the mass and calculate the area of rectangular samples of poster board. Graph mass and area data, drawing a "best-fit" line through the origin of the graph (since zero area would be zero mass – or “nothing”). Interpret the graph to find the area of irregularly shaped sample of cardstock paper.

MATERIALS:

Balance, 4 rectangles of cardstock paper, 1 irregular sample of cardstock, ruler, pencil

PROCEDURE:

1. Obtain four rectangles of poster board.

2. Find the mass of each sample of poster board and record the sample number and mass in your data table.

3. Measure the length and width of each sample (to the proper number of significant figures, REMEMBER to estimate the LAST DIGIT). Record the measurements under length and width in your data table.

4. Calculate the area (length x width) of each sample of poster board (enter the area in your data table).

5. Obtain an irregularly shaped sample of poster board. Find the mass and record the mass and sample letter in your data table.

6. Plot a graph of mass versus area for your rectangular samples. Place mass on the y-axis and area on the x-axis. Make sure to label each axis with quantity and unit, and then give your graph an appropriate title. Format the table so that it shows your data clearly.

x-axis label: area (cm^2)
y axis label: mass (g)
sample title: The Relationship Between Mass and Area of Cardstock Paper

7. Using Microsoft Excel, draw a "best-fit" line, which is a linear trendline, for your data points. Show the equation of this line on your graph.

8. Solve for the unknown using method A:
Method A: Locate the mass of your irregular sample on the line and determine its area by moving down vertically to the x-axis. Record this area in the data table.

9. Solve for the unknown using method B:
Method B: Use the equation of the trendline to find the area of the unknown. (HINT: plug in mass for y and solve the equation for x, which is area). Record this area in the data table.

10. Print out your graph for your instructor (should be size of an entire page).

DATA:

Table 1: Area and Mass of Cardstock Paper

Sample / Length (cm) / Width (cm) / Area (cm2) / Mass (g)
A
B
C
D
unknown / A)
B)

QUESTIONS AND CONCLUSIONS:

  1. Which method (A or B) do you think was better? Justify your answer.
  1. List and describe three assumptions made (also known as “sources of error”) in this activity.

1)

2)

3)