Type of tule: Ruler
Value (units) : 1/16 item
1: 1.6 inches item
2: 2.4 inches item
3: 2.3 inches item
4: 1.12 inches item
5: 1.14 inches
Procedure #1 Obtain either a straight edge ruler, preferably 12 inches, or a tape measure of any length. Determine the length value for the smallest interval between line marks, For rulers measured in inches this may be 1/16 or 1/32 of an inch. In Table 1 record the type of tool that you obtained and will be using and record the value of the smallest length interval that can be measured with the tool. Table 1 Next, select five food container or household items that are cylindrically shaped, that is, have a circular footprint when placed on a table. Select items of a variety sizes, for example, small spice containers, canned food items, or a larger container of oats. In Table 2 record for the five items the diameter and circumference to a length accuracy that was recorded in Table 1. Remember to list inside of the box the unit of measure. In the last column of Table 2 calculate the circumference of the item based upon your measured diameter using the circumference of a circle formula C=p*D. Complete Graph #1 below by plotting the measured circumference values listed in Table 2 versus the measured diameter values, the horizontal axis. Five data values will be plotted on Graph “1 and chosen ranges on the vertical and horizontal axes should be made so that the plotted values are spread across the graph and do not exceed either below or above the ranges chosen for the graph. Label the axes with event incremented numerical values at each grid line at the left of the vertical axis and below the horizontal axis. Also, label the axes with “measured circumference” or “measured diameter” and put the units used inside of parentheses. Enter the title of the graph on the line provided. When plotting the five data values use a small dot and then make a circle around the dot that has a radius equal to the length given in the value that you provided in Table 1. Graph =1 Title Determination of Slope in Graph =1 Using a straight edge draw a line through the five data points plotted on Graph w1. When drawing the line minimize to the best extent possible the distance individual data points are away from the line. Choose two data values which are closest to the line drawn and calculate the slope between those two data points using the mathematical slope formula for a two-dimensional. coordinate system n=(y2?·y1?)/(x2?+x1?). Show the details of your calculation below. Enter the calculated value in the box provided and comment on the comparison of this value with the value of p approximately 3.1415 – Copyright 2022 by Ties McMahon Complete Graph #2 below by plotting the measured circumference values listed in Table 2 versus the calculated circumference values, the horizontal axis. Five data values will be plotted on Graph #2 using the procedures mentioned for Graph #1. For this graph write commentary below the completed graph what you would have expected the graph of the data values to look like and compare with the results of the graph. Graph #2 Title Provide in the space below observations and commentary about Graph #2 above. measured circumference (units) item
1: 5.024 item
2: 7.536 item
3: 7.222 item
4: 3.52 item
5: 3.6
The Correct Answer and Explanation is :
To answer the task, we will break it into steps and address each requirement:
Step 1: Table 1
Tool: Ruler
Value of the smallest length interval: (1/16) inches.
Step 2: Table 2
The given diameters and calculated circumferences based on (C = \pi \cdot D) are:
| Item | Measured Diameter (in) | Measured Circumference (in) | Calculated Circumference (in) |
|---|---|---|---|
| 1 | 1.6 | 5.024 | (1.6 \cdot \pi = 5.0265) |
| 2 | 2.4 | 7.536 | (2.4 \cdot \pi = 7.5398) |
| 3 | 2.3 | 7.222 | (2.3 \cdot \pi = 7.2330) |
| 4 | 1.12 | 3.52 | (1.12 \cdot \pi = 3.5186) |
| 5 | 1.14 | 3.6 | (1.14 \cdot \pi = 3.5814) |
Step 3: Graph #1
This graph plots measured circumference (y-axis) against measured diameter (x-axis). The data points should lie close to a straight line because circumference is directly proportional to diameter, with the slope approximately equal to (\pi).
Step 4: Slope Determination
The slope formula is:
[
m = \frac{y_2 – y_1}{x_2 – x_1}
]
Selecting two data points close to the line, for example:
((1.6, 5.024)) and ((2.4, 7.536)):
[
m = \frac{7.536 – 5.024}{2.4 – 1.6} = \frac{2.512}{0.8} = 3.14
]
This value is approximately equal to (\pi \approx 3.1415), confirming the relationship.
Step 5: Graph #2
Graph #2 plots measured circumference (y-axis) against calculated circumference (x-axis). The data points should align closely along the line (y = x), indicating consistency between measured and calculated values.
Observations and Commentary
- Graph #1: The relationship between circumference and diameter is linear, as expected. The slope, calculated as approximately (3.14), confirms the proportionality constant (\pi).
- Graph #2: The graph shows a 1:1 correspondence between measured and calculated circumferences, indicating accuracy in measurements and calculations.
- Conclusion: Both graphs validate the geometric relationship (C = \pi \cdot D) and demonstrate that the measured data align well with theoretical expectations.
This experiment effectively demonstrates the proportional relationship between the diameter and circumference of circular objects, reinforcing the use of (\pi) in practical geometry.