The water meters in Athens and many other places measure your water usage in Cubic Feet. Most of us have very little intuition about how much water is in a cubic foot. In recent years the new water statements and rates in Athens are in terms of gallons (x 1000). The meter readings are still in cubic feet.
The point of this problem is to develop intuitive estimates of the number of gallons of water in a cubic foot, using items that might be familiar to us.
Modern Plastic One Gallon Milk Jug.
The bulk of the milk is in a more or less cubical region in the bottom of the jug. In making an estimate we can concentrate on where the bulk of the milk is rather than the diminishing spaces at the top. The base is a little over 5 inches square so it is not unreasonable to ESTIMATE the volume of the milk jug (in cubic inches) to be in a 6 x 6 x 6 cube. So how many such cubes would fit in a 12 x 12 x 12 space (a cubic foot)? We can argue with some degree of confidence for an estimate of between 7 and 8 gallons in a cubic foot.
Compare a known gallon.
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 gallon in a cubic foot. Have students estimate from the visual comparison.
The can pictured at the right is a one gallon container, roughly 4 inches by 6 inches on the bottom and slightly over 9 inches tall. Six of these would sit compactly in the bottom 9 inches of a 12 x 12 x 12 box. So these 6 gallons are about 9/12, or 3/4, of a cubic foot. The other 1/4 would be a bit less than 2 gallons so once again we have a cubic foot is between 7 and 8 gallons.
How many gallons in a cubic foot?
How many cubic inches in a gallon?
How many cubic feet of gasoline in a Studebaker gasoline tank with a capacity of 17 gallons? What's a Studebaker? (Don't laugh. I owned one of these. Gasoline was under 20 cents per gallon.)