Question 443127
As you know the volume of the sphere with radius r is:{{{V[1]=(4/3)(pi)r^3}}}, and

the volume of the cube with length a is:{{{V[2]=a^3}}}. 

To find the ratio {{{a/r}}}, we know that {{{V[2]=V[1]}}}, substituting:

{{{a^3=(4/3)(pi)r^3}}}=> {{{a^3/r^3=4*(pi)/3}}} => {{{(a/r)^3=4*(pi)/3}}}, and,

a/r=cubed root of {{{4*(pi)/3}}} or {{{a/r=(4*(pi)/3)^(1/3)=1.66}}}