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If the greatest distance between any two points on a cube is 8 inches, what is the volume of the cube, in cubic inches?  Express your answer in simplest radical form.

 Jul 19, 2022
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The greatest distance = the body diagonal  of the cube

 

8 =  sqrt  ( s^2 + s^2 + s^2)

 

8 =  sqrt (3 s^2)

 

8  =  s sqrt (3)

 

s  =  8 /sqrt (3)

 

Volume =  side^3 =    (8/sqrt (3))^3  =  [(512) / 3]  / sqrt 3  =    (  512sqrt(3)   / 9 )   in^3

 

 

cool cool cool

 Jul 19, 2022

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