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A rectangular solid, or cuboid, with sides of lengths 2, 10, and 22 is inscribed in a sphere. What is the side length of the cube that can be inscribed in that sphere?

 May 4, 2020
 #1
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A rectangular solid, or cuboid, with sides of lengths 2, 10, and 22 is inscribed in a sphere. What is the side length of the cube that can be inscribed in that sphere?

 

Face diagonal (Df) of the cuboid's side  10 x  22 is:>     Df = sqrt(22² + 100²) = 24.16609195

 

Interior diagonal (Ds) of the cuboid is:>                           Ds = sqrt(Df² + 2²) = 24.24871131

 

Ds is the diameter of a sphere and also an interior diagonal of a cube.

 

The side length of the cube (a) is:>               a = Ds / sqrt(3) = 14   indecision 

 May 4, 2020
edited by Dragan  May 4, 2020
 #2
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Geat explanation!

LuckyDucky  May 5, 2020
 #3
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Thanks, Lucky!

Dragan  May 5, 2020

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