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## A Pile of Corn

The Given: Located in Ralston, Iowa, the conical pile of 2.7 million bushels of corn was 60 feet high and 300 feet in diameter. Also, American farmers should produce 10.9 billion bushels of corn this year.

Question 1: Using the information given, estimate the size of a bushel in cubic feet? Now, consult a reference source for the actual size of a bushel.

Question 2: What would be the dimensions of the conical pile if all of the corn produced this year was pushed into a single pile? Assume that the cone has the same ratio of cone height to base diameter as the given pile.

Question 3: Dropped by an auger, the corn forms a conical pile, supposedly seeking "an angle of repose" of 22 degrees with the ground. Does this seem true given the pile of corn shown? Explain.

Question 4:Given the information and your response to the question, do you believe the article? Explain.

NOTE: For more interesting information about corn piles, consult the web site Grain Storage, which claims that for a conical pile of height h and base diameter d, the number of bushels is approximately 0.209d2h. Why does this formula suggest other problems with the article's veracity

Source: Alexei Barrionuevo's "Mountains of Corn and a Sea of Farm Subsidies," New York Times, November 9, 2005, p. 1.