Notes

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This lab involves the measurement of the area and diameter of nine coins, and the combination of this data with the coins' squared diameters to create two distinctly different graphs. I studied the relationship between the diameter and area of the coins and the relationship between the squared diameter and area of the coins.
By graphing the data, I observed that relationship between the diameter and area of the coins was roughly quadratic, and the relationship between the squared diameter and area of the coins was directly linear. The shapes of these graphs can be explained by forming an equation that best fits each line. The diameter of a circle equals 2 times the radius, therefore the area equals pi times half the radius squared. Thus, the equation for the relationship between diamter and area of the coins is y=pi(x/2)^2, where y is the area and x is the diameter. The equation for the relationship between the squared diameter and the area of the coins is y=pi(rad(x)/2)^2, where y is the area and x is the diameter squared. Since the second equation can be transformed into the first equation by squaring the rad(x), the y values in the first equation increase exponentionally compared to the geometric increase in the y values of the second equation.
The slope of the graph of the relationship between the squared diameter and area of the coins is approximately 0.741. For each one box increase of the squared diameter, the area increases by about 0.741 boxes squared.
The percent error of my results is 5.73%. One possible source of error is the uneven edges of the coins. This made it more difficult to trace the exact circumference of the coin onto the paper.