Lori Pearman
EMT 725

Problem: Gallons per cubic foot

Compare a gallon container, such as a paint can, and a box or stick structure 12 inches on a side
visually. Estimate or guess how many gallons are in a cubic foot. Have students estimate from the visual comparison.
To explore the problem of volume estimation, I found a cubic foot box and tried to guess how many gallons would fill the volume. My guess was a poor estimation of the actual volume. I guessed 3 gallons, when it was actually 7.4805 gallons. After guessing, I used my TI-85 calculator to get the conversion. It has standard conversion factors built in; however, such conversions are also available in standard references. From it, I also determined that 1 gal. = .13368 ft.^3 . Knowing this, one can manually find how many cubic inches are in one cubic foot. 1 ft. = 12 in. Therefor, cubing each side yields 1 ft.^3 = (12 in.)^3 = 1728 in.^3.
Now you can use this to determine how many cubic inches that are in one gallon.
1 gal. = 0.13368 ft.^3
= 0.13368 ft. [(1728 in.^3)/1 ft.^3] = 231 in.^3

How many cubic feet of gasoline are in a Celica tank with a capacity of 17 gallons?

1 gal. = 0.13368 ft.^3
so 17 gal. = 17 (0.13368) ft.^3 = 2.2725694 ft.^3

Possible extensions:

One extension would be to bring to the classroom several boxes each having a 1 cubic foot volume, but which have different dimensions (some of which having 12 in. on a side ). Have students guess how many gallons they think would fill each box. Then have them determine this. When they see that the volumes are the same, they will know that the volume in gallons would be the same for each of the boxes. This would give them a better understanding of what volume means, and how estimates of the volume can differ because of visual perceptions.
Another extension would be to provide boxes of different volumes. First have students estimate how many gallons are in a box of 1 ft.^3 volume. Then have them guess how many gallons would "go into" the other boxes. After guessing, they could determine the actual number of gallons (for comparison). For example, I tried making a guess about a box with dimesions of 15 X 10 X 3 inches. The volume is 450 in.^3 or .2604 ft.^3. I guessed that there were about 1.5 gal. in the 450 in.^3 box. The actual number of gallons was 1.9479 . Again, I underestimated the volume of the box (in gallons). However, because I had a better mental image now of how many gallons are in a cubic foot box, my guess was improved.

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