Question

if the sphere is incribed in a cube,then the ratio between Volume of cube and sphere.

Answer 1

If a sphere is inscribed in a cube then,
the diameter of sphere = side of the cube
Let, 
the radius of sphere = r
side of cube = s,
then,
s=2r
r=s/2
volume of cube = s³
volume of sphere = (4πr³)/3=(4π(s/2)³)/3
vol.of cube:sphere = s³/(4πs³/8)/3
                              =  (s³×3)/4πs³/8
                              = s³×3×8/4πs³
                              = 24/4π
                              = 6/π⇒6:π

Answer 2

Hey mate..
========

Given,

A sphere is inscribed in a cube .

When we visualise this particular scenerio, it will come to light that

The diameter of the sphere is equal to the each side side of a cube.

Let, each side of the cube be 'a'

And Diameter of the sphere be 'd'

So,

By the given relation, we have,

a = d..........(1)

Now,

Ratio between Volume of Cube and Volume of sphere

$\frac{a {}^{3} }{ \frac{4}{3} \pi \: r {}^{3} } \\ \\ = > \frac{a {}^{3} }{ \frac{4}{3}\pi( \frac{d}{2} ) {}^{3} } \\ \\ = > \frac{a {}^{3} }{ \frac{4}{3}\pi( \frac{a}{2} ) {}^{3} } \: \: \: \: (from \: 1) \\ \\ = > \frac{a {}^{3} }{ \frac{11a {}^{3} }{21} } \\ \\ = > \frac{21}{11}$


Thus,

Ratio between the volume of the cube to the volume of sphere is 21:11

Hope it helps !!!!