Procedure:
1. Carefully measure the diameter and circumference of each circular object and record the measurements in the table below.
Diameter |
Circum-ference |
c + d |
c – d |
C D |
C/ D |
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2. Once you have measured the circumference and diameter of each object, complete the table by finding the sum, difference, product and quotient of each pair of numbers. Let C represent the circumference and D represent the diameter. What patterns do you see, if any? Explain below.
“C+D” pattern:
“C-D” pattern:
“C*D” pattern:
“C/D” pattern:
3. We say that the circumference is a function of the length of its diameter. We write this as C(d). This doesn’t mean to multiply C times d but is an example of functional notation. The actual function is a linear one which is C(d) = pd. Where the greek letter “p” represents an irrational number that can be approximated as p = 3.14.
4. Use the relationship C = pd above to answer the following questions. Show your work
a. The circumference of a water tower is 60 feet. What is the diameter?
b. If the circumference of the water tower above is increased by 6 feet, what is the resulting increase in the diameter?
5. Here is an infamous brain teaser. Imagine a rope that is just long enough to go completely around the earth at the equator (Pretend that the earth is a perfect sphere). Now imagine that 20 feet of rope is added and somehow the rope is lifted up evenly around the equator. The rope still forms a circle but is now above the surface of the earth. Which of the following critters could walk under the rope?
a. an ant
b. a house cat
c. a dog
d. an elephant
Show your work/reasoning for your above choice(s).