CIRCUMFERENCE
STATIONS
Name: ______________________________
Group Members: __________________________________________________________________
Directions: In this station activity students will be collecting data about the
relationship between the diameter of a circle and the circumference of a
circle. Around the room there are 7 stations each with an object to be
measured. Students will be using a ruler to measure the diameter of a circle
and a piece of string, which will then measure, to obtain the circumference.
Collect this data in the following chart.
Object
Circumference (cm) Diameter (cm)
Now that the data has been collected it is time to put in a form which is
easier to interpret, graph it. As a class and with teachers help graph the data
collected. EACH student will be given a piece of graph paper and is
expected to create their own graph. All lines will be made with a ruler and
the writing will be clear and neat!!!
Let’s start:
1. With the circumference on the “Y” axis and diameter on the “X” axis come
up with an appropriate range of for each axis, as well as how far apart to space
the numbers. The graph is to use up as much of the graph paper as possible.
2. Now label each axis including the proper units.
3. At the top of the graph there should enough room to place a title.
4. For this graph there will not be a legend.
5. Now it is time to place the data points on the graph.
6. Should there be a point at the origin?
7. After all data points are on the graph make a best fit line.
Now let’s answer some questions
a. How would you describe the relationship between circumference and
diameter___________________________________________________
__________________________________________________________
b. The relationship between circumference and diameter is called directly
proportional which means is and as circumference _______________ diameter
________________.
c. Explain how you would find the circumference of a circle that has a diameter
of
15
cm
using
this
graph.
___________________________
_____________________________________________________________
d. So, what is the circumference? _______________________________
e. Using the graph, what would the diameter be if the circle had a circumference
of 40 cm? __________________________________
f. You have had plenty of practice finding the slope of a line now; find the slope
of this line, SHOW ALL WORK!!
g. In addition to finding the slope of a line we have also learned and practiced
finding an equation for a line, y=mx+b. What would an equation for this line
be? ___________________________________
h. Our graph can be used only when the diameter is between zero and our
greatest measurement. Is this true for our equation? _______________
i. Why can you use this equation for any size circle? _________________
_____________________________________________________
j. What would the circumference be of a circle with a diameter of 500 cm? Show
your work!
k. Here’s a tougher one, what would the diameter be of a circle with a
circumference of 750 cm?