Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.

Explanation

Let side of cube is `a` and radius of sphere is `r`.

As sphere exactly fit inside the cube,

`:. a = 2r`

Ratio of volume of cube to that of sphere,`V_c/V_s = a^3/(4/3pir^3)`

`V_c/V_s = (2r)^3/(4/3pir^3)`

`=>V_c/V_s = (8r^3)/(4/3pir^3) = 6/pi`

So, the required ratio is `6:pi`.