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#39235

geometry

volume

hard

120 sec

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A solid sphere is perfectly inscribed within a cube, meaning it touches the center of each face of the cube. If the volume of the cube is $V_{C}$ , what is the volume of the sphere in terms of $V_{C}$ ?

A.

$\frac{π V _{C}}{6}$

B.

$\frac{V _{C}}{6}$

C.

$\frac{4}{3} π V_{C}$

D.

$\frac{2}{3} π V_{C}$