SOLUTION: A cube with volume 8 cubic centimeters is inscribed in a sphere so that each vertex of the cube touches the sphere. What is the length of the diameter, in centimeters, of the sphe

Algebra ->  Bodies-in-space -> SOLUTION: A cube with volume 8 cubic centimeters is inscribed in a sphere so that each vertex of the cube touches the sphere. What is the length of the diameter, in centimeters, of the sphe      Log On


   

Question 307888: A cube with volume 8 cubic centimeters is inscribed in a sphere so that each vertex of the cube touches the sphere. What is the length of the diameter, in centimeters, of the sphere?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
the diagonal of the cube is the diameter of the sphere

the edge of the cube is 2 (the cube root of 8)

the diagonal of a rectangular prism is ___ sqrt(L^2 + W^2 + H^2)

in this case ___ d = sqrt(2^2 + 2^2 + 2^2) = 2 sqrt(3)