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A box contains one sphere of radius 2 and four spheres of radius $2$, as shown below.  The sphere of radius 2 is tangent to five sides of the box, and each sphere of radius $2$ is tangent to three sides of the box.  Find the volume of the box.

 Dec 31, 2024
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The volume of the box is 32 + 12*sqrt(3).

 Dec 31, 2024

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