Difference between revisions of "2008 AMC 12B Problems/Problem 11"
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A cone-shaped mountain has its base on the ocean floor and has a height of 8000 feet. The top <math>\frac{1}{8}</math> of the volume of the mountain is above water. What is the depth of the ocean at the base of the mountain in feet? | A cone-shaped mountain has its base on the ocean floor and has a height of 8000 feet. The top <math>\frac{1}{8}</math> of the volume of the mountain is above water. What is the depth of the ocean at the base of the mountain in feet? | ||
Revision as of 12:48, 15 February 2021
Problem
A cone-shaped mountain has its base on the ocean floor and has a height of 8000 feet. The top 
of the volume of the mountain is above water. What is the depth of the ocean at the base of the mountain in feet?
Solution
In a cone, radius and height each vary inversely with increasing height (i.e. the radius of the cone formed by cutting off the mountain at 
feet is half that of the original mountain). Therefore, volume varies as the inverse cube of increasing height (expressed as a percentage of the total height of cone):
Plugging in our given condition, 
.
.
See Also
| 2008 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 10 |
Followed by Problem 12 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
