Name ______________________________
Ms. Sabbatino
Date ___________
Period _________
Lab #1: Relationships within a Circle
Goals:
To use a graph to derive formulas and mathematical constants
Background:
IN A PARAGRAPH address the following in full sentences
- Define the following terms in your own words
o circumference
o radius
o diameter
- Tell your reader which letter you will use to represent each of the terms above
- Tell your reader what units you will be using to measure each quantity.
Finish the paragraph below following the example sentence.
“In this lab, the circumference of a circle will be defined as the distance around the
outer edge of a circle. It will be represented in formulas by c and measured in
centimeters.” ____________________________________________________________
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Materials:
- Ruler
- String
- Various sized circles
Lab Setup:
Draw a diagram that shows your setup. Make sure all of your materials appear labeled in
your diagram.
Procedure:
1. Using a ruler, measure the diameter of a circular object and enter it into the data
table.
2. Calculate the radius of that circle and enter that into the data table.
3. Using a piece of string, wrap it around the outer edge of the circle and mark off
where it reaches back to where you started.
4. Measure the length of that string and record that in your data table as the
circumference.
5. Repeat this process for five more circles of different shapes.
Data:
Circle description
Diameter (
)
Radius (
)
Circumference (
Analysis:
1. On the first graph on the following page, graph the diameter of each circle vs. the
circumference of the circle.
2. If the data looks linear, USE A RULER to draw a line of best fit through the data.
(Include the point 0,0 if it is true that a circle with a diameter of 0cm would have
a circumference of 0cm.)
3. Choose two points that are ON YOUR LINE OF BEST FIT and draw a box
around them. The farther apart these points, the better.
4. Use these two points to calculate the slope of your line of best fit.
a. Write the formula for slope
b. Plug in each value with the units (look at your axis for the units)
c. Calculate the slope and report the answer with units (if there are any)
5. Since the data is linear, you can derive a formula from this graph using the
general equation of a line. Usually, the equation for a line is y= mx + b.
o You want to replace the general ‘y’ in the equation above with the letter
you chose to represent the value on your y-axis.
o You want to replace the general ‘m’ in the equation above with the value
you calculated as your slope of the best fit line.
o You want to replace the general ‘x’ in the equation above with the letter
you chose to represent the value on your x-axis.
o You want to replace the general ‘b’ in the equation above with the value of
your y-intercept on the graph.
6. Look at the equation you have derived, does it look familiar? What should the
slope of that graph be? (which value usually would take the place of ‘m’?)
)
7. Using the ‘accepted’ value for the slope (pi = 3.14) in this case, calculate the
percent error of your slope using the formula below. Make sure you rewrite the
formula, plug in all the numbers, then answer with units.
accepted  actual
%error 
 100%
accepted
8. Repeat ALL STEPS for the graph of radius vs circumference graph.
Circumference (cm)
Graph of Circumference vs. Diameter for a Circle
Diameter (cm)
Slope Calculation:
Point 1: (
,
)
Point 2: (
,
)
Formula:
Answer with units:
Plug in with units:
-----------------------------------------------------------------------------------------------------------Formula Derivation
Y
=
m
x
+
b
____ = ______ _______ + _______
-----------------------------------------------------------------------------------------------------------Percent Error Calculation
Accepted value: __________
Formula:
Answer
Your value: _____________
with units:
Plug in with units:
Circumference (cm)
Graph of Circumference vs. Radius for a Circle
Radius (cm)
Slope Calculation:
Point 1: (
,
)
Point 2: (
,
)
Formula:
Answer with units:
Plug in with units:
-----------------------------------------------------------------------------------------------------------Formula Derivation
Y
=
m
x
+
b
____ = ______ _______ + _______
-----------------------------------------------------------------------------------------------------------Percent Error Calculation
Accepted value: __________
Formula:
Answer
Your value: _____________
with units:
Plug in with units:
Conclusion:
IN A PARAGRAPH address the following in full sentences.
- For the diameter of a circle,
o Restate the goals
o Report your results
o Offer your percent error
- For the radius of a circle,
o Restate the goals
o Report your results
o Offer your percent error
- Offer a source of error for the lab overall (stating human error DOES NOT
COUNT)
- Suggest another investigation the reader could do that would further their
understanding of this topic.
One goal of this lab was to determine the relationship between the diameter and
circumference of a circle. We found that there was a linear relationship between the
diameter and circumference of a circle. This linear relationship allowed us to derive the
formula c=πd. The slope of the line was found to be _________ and the actual value of
pi is 3.14159… Our value had a _________ % error from the accepted value.
A second goal of the lab was to determine the relationship between radius and
circumference of a circle. _________________________________________________
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