Describe what happens to the surface area to volume ratio for larger and larger cubes.

Measure
the volume here

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Figure 1.4

3. Use
a graduated cylinder to measure the volume of water in each of the three
containers. Be sure to get all the water into the graduated cylinder.
Record the water volume of each container in milliliters (mL) in row 8 of the
data table.

4. Calculate
the ratio of cubic centimeters (cm3)
to mL for each container by dividing the volume in cubic centimeters (row 4
data) by the volume in milliliters (row 8 data). Record your findings in the
data table.

5.
Calculate the ratio of mass per
unit volume for each container by dividing the mass in grams (row 7 data) by
the volume in milliliters (row 8 data). Record your results in the data table.

6. Make
a graph of the mass in grams (row 7 data) and the volume in milliliters (row 8
data) to picture the mass per unit volume ratio found in step 5. Put the volume
on the x-axis (horizontal axis) and the mass on the y-axis (the
vertical axis). The mass and volume data from each container will be a data
point, so there will be a total of three data points.

7. Draw
a straight line on your graph that is as close as possible to the three data
points and the origin (0, 0) as a fourth point. If you wonder why (0, 0) is
also a data point, ask yourself about the mass of a zero volume of water!

8.
Calculate the slope of your graph. The slope of a line is the change in rise
divided by the change in run.
Mathematically slope=

9. Calculate your
experimental error. Use 1.0 g/mL (grams per milliliter) as the accepted value.

10.
Density is defined as mass per
unit volume, or mass/volume. The slope of a straight line is also a ratio,
defined as the ratio of the change in the y-value per the change in the x-value.
Discuss why the volume data was placed on the x-axis and mass on the y-axis
and not vice versa.

11.
Was the purpose of this lab
accomplished? Why or why not? (Your answer to this question should show
thoughtful analysis and careful, thorough thinking.)

Results

1. What is a ratio?
Give several examples of ratios in everyday use.

2. How is the value of? obtained? Why does?not have units?

3. Describe
what happens to the surface area to volume ratio for larger and larger cubes.
Predict if this pattern would also be observed for other geometric shapes such
as a sphere. Explain the reasoning behind your prediction.

4. Why does
crushed ice melt faster than the same amount of ice in a single block?

5. Which
contains more potato skins: 10 pounds of small potatoes or 10 pounds of large
potatoes? Explain the reasoning behind your answer in terms of this laboratory
investigation.

6. Using your own words, explain the meaning of
the slope of a straight-line graph. What does it tell you about the two graphed
quantities?

7. Explain
why a slope of mass/volume of a particular substance also identifies the
density of that substance.

Problems

An aluminum block that is 1 m× 2 m× 3 m has a mass of 1.62× 104
kilograms (kg). The following problems concern this aluminum block:

2 m

One

face

1 m

3 m

Figure 1.5

l. What is the
volume of the block in cubic meters (m3)?

2. What are the
dimensions of the block in centimeters (cm)?

3. Make a sketch
of the aluminum block and show the area of each face in square centimeters (cm2).

4. What is the
volume of the block expressed in cubic centimeters (cm3)?

5. What is the
mass of the block expressed in grams (g)?

6.
What is the ratio of mass (g) to
volume (cm3) for
aluminum?

7. Under
what topic would you look in the index of a reference book to check your answer
to question 6? Explain.

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