Difference between revisions of "2000 AIME I Problems/Problem 8"
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== Problem == | == Problem == | ||
| + | A container in the shape of a right circular cone is 12 inches tall and its base has a 5-inch radius. The liquid that is sealed inside is 9 inches deep when the cone is held with its point down and its base horizontal. When the liquid is held with its point up and its base horizontal, the liquid is <math>m - n\sqrt [3]{p},</math> where <math>m,</math> <math>n,</math> and <math>p</math> are positive integers and <math>p</math> is not divisible by the cube of any prime number. Find <math>m + n + p</math>. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2000|n=I|num-b=7|num-a=9}} | |
Revision as of 18:30, 11 November 2007
Problem
A container in the shape of a right circular cone is 12 inches tall and its base has a 5-inch radius. The liquid that is sealed inside is 9 inches deep when the cone is held with its point down and its base horizontal. When the liquid is held with its point up and its base horizontal, the liquid is ![$m - n\sqrt [3]{p},$](http://latex.artofproblemsolving.com/1/5/8/1586f2bca69882cdcb09b653822a61d6a5931db7.png)
where 
and 
are positive integers and is not divisible by the cube of any prime number. Find 
.
Solution
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See also
| 2000 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
