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1960 AMC 12 Question 23

AMC12 · 1960 AMC 12

Question 23

The radius $R$ of a cylindrical box is $8$ inches, the height $H$ is $3$ inches. The volume $V=\pi R^2H$ is to be increased by the same fixed positive amount when $R$ is increased by $x$ inches as when $H$ is increased by $x$ inches. This condition is satisfied by:
  1. no real value of $x$
  2. one integral value of $x$
  3. one rational, but not integral, value of
    $x$
  4. one irrational value of $x$
  5. two real values of $x$