Bunuel wrote:

A cube with a volume of 64 cubic inches is inscribed within a sphere such that all 8 vertices of the cube are on the sphere. What is the circumference of the sphere, in inches?

A. 2π√2

B. 2π√3

C. 4π√2

D. 4π√3

E. 8π√2

In case of a cube inscribed within a sphere, the cube's diagonal (largest distance between any 2 points on the cube) and the sphere's diameter (largest distance between any 2 points on the sphere) should be equal.

We also know that the diagonal for a cube = \(\sqrt{3}*Side\)

As the volume of the cube = 64 cu. inches, its sides should be 4 inches each.

Thus diagonal = \(4\sqrt{3}\) = Diameter of the sphere.

Thus radius = \(2\sqrt{3}\)

=> Circumference of the sphere = \(2π*2\sqrt{3}\) = \(4π√3\)

Should be Option D.