Circle Area Puzzles

This puzzle involves measuring sizes and area on web pictures. Our unit of multi-media length (a fuller) is:

Our unit of multi-media area (a fuller²) is:

The game in this puzzle is to compare the distance across a circle to the area enclosed by the circle. To find the area enclosed by the below red circles, you need to total the full and fractional fuller² enclosed by the circle. The fuller² that are essentially fully inside the circle have been colored green for you. The fuller² that are only partially in the circle have been colored yellow -- you need to judge what fraction is enclosed. Sometimes I've counted the number of green fuller² for you to save time.

Your Name:

Circle 1

Number of green fuller²:

Sum of fractional yellow fuller²:

Circle area in fuller²:

Distance across circle in fuller:

Circle 2

Number of green fuller²:

Sum of fractional yellow fuller²:

Circle area in fuller²:

Distance across circle in fuller:

Circle 3

Number of green fuller²:

Sum of fractional yellow fuller²:

Circle area in fuller²:

Distance across circle in fuller:

Quarter Circle 4

The below is just ¼ (1/4) of a circle; You'll need to adjust your measurements to get the total area enclosed and the total distance across.

Number of green fuller²:

Sum of fractional yellow fuller²:

Total area in complete circle in fuller²:

Total distance across complete circle in fuller:

Rupert, a student in Physics 191, decided to apply the techniques of graphical analysis described in the Lab Manual. He had been a carpet layer during the summer and was primarily interested in areas. So he made a graph using the areas and sizes of the measured figures and obtained a straight line with a slope of 0.78.

Explain what graph he drew and how he got that value for the slope.

Hint: Rupert put the area on the y-axis. He did not try to log-transform any variables. (Note a log-log plot could also make a straight line, but with a slope of 2.)

Big Hint: Rupert has correctly reported that the slope has no units.

Feel free to use this on-line plot/fit tool.