Inquiry: How is the circumference of a circle related to its diameter?
Step 1: Use the string at your table to measure the circumference of each circular item. Wrap the string around the item, and then
open up the string and measure the piece of string using the centimeter side of the ruler. Name each item and record the
measurements in the table below.
Step 2: Measure the diameter of each item (do the best you can to go across the center). Record this measurement in the table.
Object
Circumference (C)
Diameter (d)
𝒄
𝒅
Step 3: Use a calculator to find the ratio of the circumference to the diameter of each of your items. Round each answer to the nearest
hundredth.
Work with your table to answer the following questions:
𝒄
1. Describe the ratio for the values you calculated.
𝒅
𝒄
2. What is the fancy name (symbol) for the ratio of ?
𝒅
So
3. What happens when you multiply the diameter by the ratio
𝒄
𝒅
𝒄
𝒅
𝒊𝒔 𝒂𝒍𝒔𝒐 𝒌𝒏𝒐𝒘𝒏 𝒂𝒔 ____?
for each item?
4. Write a formula for finding circumference.
5. The radius of a circle is half of its diameter; therefore it takes two radii to make one diameter. Write a formula that relates the
circumference of a circle to its radius r.
𝑐𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
=
𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟
Formula for Circumference (with diameter)
Formula for Circumference (with radius)