What is the ratio of the volume of cube and the smallest sphere that could contain it?

You need to fit the sphere inside the cube, hence, the diameter of sphere needs to be equal to the side of cube such that:

`D = a`

D represents the diameter of the sphere

a represents the side of the cube

You need to remember the formula of volume of sphere such that:

`V = (4pir^3)/3`

You need to remember that `r = D/2 =gt r^3 = (D^3)/8`

Substituting `(D^3)/8`  for`r^3`  in formula of volume of sphere yields:

`V = (4pi*(D^3)/8)/3`

`V = (pi*(D^3)/2)/3 =gt V = (pi*(D^3))/6`

Notice that D = a, hence, you need to substitute a for D in formula of volume of sphere such that:

`V = (pi*(a^3))/6`

You need to remember the formula of volume of the cube such that:

`v = a^3`

You need to evaluate the ratio `v/V`  such that:

`v/V = (a^3)/((pi*(a^3))/6)`

Reducing by `a^3`  yields:

`v/V = 6/pi`

Hence, evaluating the ratio of volumes under given conditions yields `v/V = 6/pi.`