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A sphere is inscribed in a cube with edge length 9 inches. Then a smaller cube is inscribed in the sphere. How many cubic inches are in the volume of the inscribed cube? Express your answer in simplest radical form.

 Mar 27, 2019
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The radius of the sphere will be 9 inches

 

And this will be the length of the  "long" diagonal drawn from the bottom vertex of the small cube to the oppositie top vertex

 

And we can find the edge length , e, of this cube as

 

e^2 + 2e^2  = 9^2

 

3e^2  = 81

 

e^2  = 27

 

e = √27

 

So...the volume of the smaller cube  is  

 

e^3  = (√27)^3 =  

 

27√27 =

 

81√3  in^3

 

 

cool cool cool

 Mar 27, 2019

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