Difference between revisions of "2022 AIME II Problems/Problem 3"
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| + | ==Problem== | ||
| + | A right square pyramid with volume <math>54</math> has a base with side length <math>6.</math> The five vertices of the pyramid all lie on a sphere with radius <math>\frac mn</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n</math>. | ||
| + | |||
| + | ==Solution== | ||
| + | |||
| + | ==See Also== | ||
| + | {{AIME box|year=2022|n=II|num-b=2|num-a=4}} | ||
| + | {{MAA Notice}} | ||
Revision as of 23:11, 17 February 2022
Problem
A right square pyramid with volume 
has a base with side length 
The five vertices of the pyramid all lie on a sphere with radius 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
See Also
| 2022 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
