Question 18.38

8. Recent dollar coins (Presidential, Susan B. Anthony, Sacagawea) have been largely rejected by the public, which finds them too small and too light. Suppose that you are appointed to the U.S. Citizens Coinage Advisory Committee and commissioned to design a new $5 coin. (Whom should it depict?) The sole requirement is that it be made of the same material as the quarter but weigh 4 times as much. A quarter can be described geometrically as a circular cylinder approximately 24.26 mm in diameter and 1.75 mm thick. Because your new dollar should weigh 4 times as much, it needs to have 4 times the volume of a quarter. [The formula for the volume of a cylinder is , where is the height and is the diameter.]

  1. A member of your public advisory panel suggests just doubling the diameter and doubling the thickness. What do you tell this individual, in the most diplomatic terms?
  2. If you double the diameter, how thick does the coin need to be?
  3. Another member feels that the result of part (b) would be inconveniently large and proposes instead to scale up the quarter proportionally. (She studied a previous edition of this book.) What would the dimensions be for this coin?
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Sacagawea dollar.
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Presidential series dollar. Coins shown actual size (26.50 mm in diameter, 2.00 mm thick).