## 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.

### 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.