Relationship between Circumference and Diameter of a Circle
Relationship between
Circumference and
Diameter of a Circle
Name ____________________________
Class ____________________________
Student Worksheet
Problem 1: ‘Circle, circles, everywhere’
1. Open up the PTE-Geom-DiaCir.tns document on your TI-Nspire™ math and science
learning handheld by pressing c 7 for Home 7:My Documents.
2. Scroll to the document, and press ·.
•
Figure 1 shows what the PTE-Geom-DiaCir.tns document looks like when it is open on your
TI-Nspire™ handheld.
Figure 1
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Press
/ ¢ on the NavPad cursor control to move to page 1.2. On page 1.2 of Problem 1,
you will find a circle with a measured radius and circumference (Figure 2).
3. Drag the radius point to see the values change.
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To drag, move the cursor to the point, press and hold the
x key until the “hand” closes,
and use the NavPad to move the point around the screen.
Figure 2
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Relationship between Circumference and Diameter of a Circle
Measurement
We will now determine the diameter. First we need to enter some text.
4. Press b 1 5 for Menu 1:Actions, 5:Text.
·.
At the text insertion point, type 2r, and press · (Figure 3).
5. Move the pointer to an empty location, and press
6.
Figure 3
7. Next, press b 1 7 for Menu 1: Actions, 7:Calculate, move the cursor to select
the text just entered (2r), and then select the radius measurement.
8. Move this calculation closer to the 2r text on the screen (Figure 4).
Figure 4
9. Once again, drag the radius point to see values change.
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Relationship between Circumference and Diameter of a Circle
Ratio of Circumference to Diameter
10. To explore the ratio of circumference and diameter, press b 1 5 for Menu
1:Actions, 5:Text, move the cursor to an empty location, and type the text C/d onto the
screen.
11. Press b 1
7 for Menu 1:Actions, 7:Calculate.
12. Select, in this order, the expression C/d, then the circumference measurement, and
finally the diameter measurement.
13. Move the calculation closer to the C/d text (Figure 5).
Figure 5
14. Drag the radius point back and forth along the segment to see which measurements
change and which remain the same (as in Figure 6).
Figure 6
15. Answer question 1 at the end of this worksheet, and then proceed to problem 2.
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Relationship between Circumference and Diameter of a Circle
Problem 2: Lists & Spreadsheet
A Lists & Spreadsheet application will be used to save the data as the radius point moves. In
the Lists and Spreadsheet application, there are 3 lists: One tracks the diameter (list d),
another tracks the circumference (list C), and the third tracks the circumference/diameter
relationship. One set of data is given in Figure 7 below.
Figure 7
16. To collect data, press / e until the Graphs & Geometry work area is highlighted.
17. Drag the radius to a new position.
18. Press / ^ to capture the data and record it in the Lists and Spreadsheet work area.
19. Repeat with five different radii values.
20. Answer questions 2 and 3 at the end of this worksheet.
Graphical Representation
21. To see the graphical representation, press / ¢ to advance to the next page.
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A scatter plot has been set up to show the data (See Figure 8).
Figure 8
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Relationship between Circumference and Diameter of a Circle
22. Press b 4 9 for Menu 4:Window, 9:Zoom-Data to see a more appropriate
window (See Figure 9).
Figure 9
23. Answer questions 4 to 6 at the end of this worksheet.
24. To fit a line to the data, press b
(See Figure 10).
6 4 for Menu, 6:Points & Lines menu, 4:Line
Figure 10
25. Move to one data point, press ·, and then press · again on another point.
26. Press b
7 3 for Menu, 7:Measurement, 3:Slope, move to the line, and press
·.
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Relationship between Circumference and Diameter of a Circle
27. Find the equation of the line by selecting b
6:Coordinates and Equations (Figure 11).
1 6 for Menu, 1:Actions,
Figure 11
28. Answer question 7, and then proceed to Problem 3.
Problem 3: Radius and Area
In problem 3, you are given the same circle with only the radius measured.
29. Press b
7 2 for Menu, 7:Measurement, 2:Area.
30. Move the cursor to the circle, and press Enter or click to select it.
31. Move the measurement to the left corner (See Figure 12).
Figure 12
32. Drag the radius point to see the values change. Proceed to Problem 4.
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Relationship between Circumference and Diameter of a Circle
Problem 4: Lists & Spreadsheet
33. The Lists & Spreadsheet application will track the data for the radius and the area
(Figure 13).
Figure 13
34. To collect more data, press /
e to move to the Graphs & Geometry work area.
35. This time, we will use automated data capture. Drag the radius point to get more data
which populates the lists automatically (Figure 14).
Figure 14
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To see the graphical representation on your TI-Nspire™ handheld, move to page 4.2 which
shows the scatter plot of area versus radius.
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Relationship between Circumference and Diameter of a Circle
36. Press b 4 9 for Menu 4:Window, 9:Zoom-Data to see a more appropriate
window (Figure 15).
Figure 15
37. Answer question 8 at the end of this worksheet.
Graph the Function
38. Press b
3 1 for Menu, 3:Graph Type, 1:Function.
39. Enter the function f1(x) = x^2, and press · (Figure 16).
Figure 16
40. Press d to move out of the entry line and see a cursor on the graph.
41. Transform the function by grabbing the curve with the x and moving the curve.
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If the four-directional cursor appears, the curve will translate; and if the two-directional
cursor appears, the curve will stretch.
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Relationship between Circumference and Diameter of a Circle
42. Manipulate the curve to get the best fit (Figure 17).
Figure 17
43. Answer question 9 at the end of this worksheet.
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Relationship between Circumference and Diameter of a Circle
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Relationship between Circumference and Diameter of a Circle
Answer the Following Questions
1. Which measurements are changing? Which measurements are staying the same?
2. Make a conjecture about Column C. Use the words of circumference and diameter in
your conjecture.
3. Long ago, mathematicians named the circumference/diameter ratio with the
Greek letter π (pi).
Complete the conjecture: If C is the circumference and d is the diameter of a circle, then
there is a number π such that C = ______________.
Because d = 2r, where r is the radius, then C = ____________.
4. What pattern are the plotted points?
5. What type of curve would be a good fit for the plotted points?
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Relationship between Circumference and Diameter of a Circle
6. In which quadrant do all of the points lie? Why?
7. What does the slope represent?
8. What type of curve does the area versus radius appear to be?
9. What does the vertical stretch of the function represent?
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