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LINEAR MODELS CIRCLE CIRCUMFERENCE vs. DIAMETER

The diameter of a circle is the length across the circle measured directly through the center. The circumference of a circle is the length all the way around the outside edge of the circle. In this activity you will compare the diameter and circumference of several circular objects.

1. Measure & record the diameter and circumference of at least ten different circles TO THE NEAREST 10TH OF A CENTIMETER.

2. Now calculate circumference divided by diameter, and record this in the appropriate column.

|Circular Object |Diameter (cm) |Circumference (cm) |Circumference ÷ Diameter |

| |(measure to nearest 10th of cm) |(measure to nearest 10th of cm) |(decimal) |

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Use the following graph paper to graph your data first! Then answer the questions:

Graphing your Data:

1. Label each axis of your graph. We want diameter (in cm) on the horizontal or side-to-side axis, and circumference (in cm) on the vertical or up-and-down axis.

2. Start numbering both axes at ZERO! Then label numbers along each axis, going up by increments that will make it so you can reach the highest values for diameter and circumference from the data.

3. Plot the data.

4. USING A RULER, sketch a “best fit line” that is closing to going through the center of all of your data points.

Circumference vs Diameter Graph

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1. Look back at your table of data. Do you see any pattern(s) emerging? If so, what pattern(s) do you see? Especially look at the ratio between circumference and diameter.

2. Does your “best-fit line” cross either axis? Where does it cross and what does this mean?

3. An average CD has a diameter of about 12 cm. Use your best-fit line to predict the circumference of a CD ROM.

4. Ms. Gamez has a lamp shade whose circumference is about 75 cm. Use your line to find out the diameter of this lamp.

5. Write a ratio that is your best estimate for the SLOPE of the best-fit line. Show your numbers below. Divide them on the calculator to get a decimal:

SLOPE = RISE = _________________ =

RUN

6. Read the Y-INTERCEPT of your best-fit line off your graph and record its value below.

Y-INTERCEPT =

7. Remember ALL LINES have the formula y = mx + b where “m” and “b” represent different numbers. Write the equation for YOUR best-fit line below.

y = _________ x + ________

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