SOLUTION: A cube is inscribed in a sphere with diameter 9 inches. What is the volume of the cube?

Question 589243: A cube is inscribed in a sphere with diameter 9 inches. What is the volume of the cube?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The longest distance between vertices in a cube is times the side of the cube.

REASON:
The diagonal of one of the faces of a cube is the hypotenuse of a right triangle that has for legs the sides of that face of the cube, of length s. So the length of the diagonal of a face is

That diagonal and the adjacent edge from another face for a right triangle, with leg lengths and . The hypotenuse is the diagonal of the cube, and its length is

If the cube is incribed in a spere of diameter 9 inches, the cube has a 9 inch diagonal and
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The volume of a cube with a side length of is
cubic inches
(approximately 140.3 cubic inches).
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