What is the ratio of the volume of the cube to that of the cylinder ........

Quantitative Aptitude (CDS) Mensuration 3D

Direction: Consider the following for the next three (03) items :
A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.

What is the ratio of the volume of the cube to that of the cylinder ?

4:3

21:16

14:11

45:32

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Explanation:

The top view of the given assembly will look like the figure above
Outermost is the sphere. Inside that there is a cube and within that there is a cone and cylinder with same radius.
Here side of cube = a
Diameter of Sphere = body diagnol = √3 a
Radius of sphere = √3 a/2 = r1
Height of Cylinder = Height of cone = side of cube = a = h
Radius of cylinder = Radius of cone = side of cube/2 = a/2 = r2 (as shown in the figure)

$\frac{Vcube}{Vcylinder} = \frac{a^{3}}{\pi r2^{2}h}$