2005 AMC 12B Problems/Problem 16

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?

$\mathrm (A)\ \sqrt{2} \qquad \mathrm (B)\ \sqrt{3} \qquad \mathrm (C)\ 1+\sqrt{2}\qquad \mathrm (D)\ 1+\sqrt{3}\qquad \mathrm (E)\ 3$

Solution

The eight spheres are formed by shifting spheres of radius $2$ and center $(0, 0, 0)$ $\pm$ 1 in the $x, y, z$ directions.

Page

Toolbox

Search

2005 AMC 12B Problems/Problem 16

Problem

Solution

See also