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2008 AMC 12B Question 11

AMC12 · 2008 AMC 12B

Question 11

A cone-shaped mountain has its base on the ocean floor and has a height of $8000$ feet. The top $\tfrac{1}{8}$ of the volume of the mountain is above water. What is the depth of the ocean at the base of the mountain, in feet?
  1. $4000$
  2. $2000(4 - \sqrt{2})$
  3. $6000$
  4. $6400$
  5. $7000$