Bunuel
What of the following is the closest to the square of the volume of a cube that is inscribed in a sphere with a radius of 1?
(A) 2
(B) 5/2
(C) 3
(D) 7/2
(E) 4
For a cube inscribed in a sphere,
the longest diagonal of cube = Diamager of SphereLongest Diagonal of Cube \(= a√3\) where a is the side of the cube
Now, \(a√3 = 2*1\)
i.e .\(a = \frac{2}{√3}\)
Now, volume of the cube \(= a^3 = (\frac{2}{√3})^3 = \frac{8}{3√3}\)
Square of the volume = \((\frac{8}{3√3})^2 = \frac{64}{27} ≈ 2.37\)
(A) 2
(B) 5/2 =2.5
(C) 3
(D) 7/2 =3.5
(E) 4
i.e. Answer: Option B
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