A rectangular solid, $x$ by $y$ by $z,$ is inscribed in a sphere so that all eight of its vertices are on the sphe

A rectangular solid, $x$ by $y$ by $z,$ is inscribed in a sphere so that all eight of its vertices are on the sphere. If $x, y$ and $z$ are positive integers, and the radius of the sphere is $\dfrac{\sqrt{14}}2,$ what is the volume of the rectangular solid?

A. 6
B. 11
C. 12
D. 18
E. 22

Answer: A

Source: GMAT Club Tests

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