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A sphere is inscribed in a unit cube. A smaller cube is then inscribed within the sphere. What is the side length of the smaller cube?

 Apr 17, 2020
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The diameter of the sphere will be 1.

The inscribed cube will have a distance from one vertex to its opposite vertex the same as the diameter of the sphere,

so this distance is also 1.

 

If the inner cube has each dimenstion called 'x', the distance from one vertex to its opposite vertex can be found

by using this equation:  d2  =  l2 + w2 + h2     or     d2  =  x2 + x2 + x2 

Since  d = 1                                                             12  =  3x2

                                                                                  1  =  3x2

                                                                                 x2  =  1/3

                                                                                   x  =  sqrt(1/3)   or   sqrt(3) / 3

 Apr 17, 2020

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