Difference between revisions of "2001 AIME II Problems/Problem 15"
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== Problem == | == Problem == | ||
| + | Let <math>EFGH</math>, <math>EFDC</math>, and <math>EHBC</math> be three adjacent square faces of a cube, for which <math>EC = 8</math>, and let <math>A</math> be the eighth vertex of the cube. Let <math>I</math>, <math>J</math>, and <math>K</math>, be the points on <math>\overline{EF}</math>, <math>\overline{EH}</math>, and <math>\overline{EC}</math>, respectively, so that <math>EI = EJ = EK = 2</math>. A solid <math>S</math> is obtained by drilling a tunnel through the cube. The sides of the tunnel are planes parallel to <math>\overline{AE}</math>, and containing the edges, <math>\overline{IJ}</math>, <math>\overline{JK}</math>, and <math>\overline{KI}</math>. The surface area of <math>S</math>, including the walls of the tunnel, is <math>m + n\sqrt {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 square of any prime. Find <math>m + n + p</math>. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2001|n=II|num-b=14|after=Last Question}} | |
Revision as of 00:46, 20 November 2007
Problem
Let 
, 
, and 
be three adjacent square faces of a cube, for which 
, and let 
be the eighth vertex of the cube. Let 
, 
, and 
, be the points on 
, 
, and 
, respectively, so that 
. A solid 
is obtained by drilling a tunnel through the cube. The sides of the tunnel are planes parallel to 
, and containing the edges, 
, 
, and 
. The surface area of , including the walls of the tunnel, is 
, where 
, 
, and 
are positive integers and is not divisible by the square of any prime. Find 
.
Solution
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See also
| 2001 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
