Explore
11-3
MAIN IDEA
Find a relationship
between circumference
and diameter.
Measurement Lab
Circumference of Circles
In this lab, you will investigate how the circumference,
or the distance around a circle, is related to its
diameter, or the distance across a circle through
its center.
Use a ruler to measure the diameter of
a circular object. Record the length
in a table like the one shown below.
Object
Diameter (cm)
Circumference (cm)
Make a small mark at the edge of the circular object.
Place a measuring tape on a flat surface. Place the mark
you made on the circular object at the beginning of the
measuring tape. Roll the object along the tape for one
revolution, until you reach the mark again.
Record the length in the table. This is the circumference.
Repeat this activity with circular objects of various sizes.
ANALYZE THE RESULTS
1. For each object, divide the circumference by the diameter. Add
another column to your table and record the results. Round to the
nearest tenth if necessary. See students’ work.
2. What do you notice about the ratio of each circumference to each
diameter? They are slightly greater than 3.
3. Graph the ordered pair (diameter, circumference) on a coordinate
plane for each object. What do you notice?
4. Use the graph to predict the circumference of a circular object that has
a diameter of 18 centimeters. Sample answer: about 56.5 cm
3. See students’ graphs.
All points lie on a
diagonal line.
6. Sample answer: about
45 × 3.1 or 139.5 cm
5. MAKE A CONJECTURE Write a rule describing how you would find the
circumference C of a circle if you know the diameter d.
Sample answer: C ≈ 3.1d
6. Use your rule to approximate the circumference of a circular object
that has a diameter of 45 centimeters.
Explore 11-3 Measurement Lab: Circumference of Circles
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