Difference between revisions of "2005 AMC 12B Problems/Problem 16"
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== Solution == | == Solution == | ||
| − | The eight spheres are formed by shifting spheres of radius <math>2</math> and center <math>(0, 0, 0)</math> <math>\pm 1</math> in the <math>x, y, z</math> directions. | + | The eight spheres are formed by shifting spheres of radius <math>2</math> and center <math>(0, 0, 0)</math> <math>\pm 1</math> in the <math>x, y, z</math> directions. Hence, the centers of the spheres are <math>(\pm 1, \pm 1, \pm 1)</math>. |
== See also == | == See also == | ||
* [[2005 AMC 12B Problems]] | * [[2005 AMC 12B Problems]] | ||
Revision as of 18:25, 12 September 2010
Problem
Eight spheres of radius 1, one per octant, are each tangent to the coordinate planes. What is the radius of the smallest sphere, centered at the origin, that contains these eight spheres?
Solution
The eight spheres are formed by shifting spheres of radius 
and center 
in the 
directions. Hence, the centers of the spheres are 
.
