Question 264316
{{{v=(4/3)pi*r^3}}}
{{{and}}}
{{{v=x^3}}}


DIAMETER is {{{d=2r}}}
{{{r=d/2}}}
{{{v=(4/3)pi(d/2)^3}}}
{{{v=(4/3)(1/8)pi*d^3}}}
{{{v=(1/6)pi*d^3}}}


The two EQUAL volumes, as given
{{{(1/6)pi*d^3=x^3}}}
{{{d^3=(6/pi)x^3}}}

{{{(d^3)/(x^3)=6/pi}}}

{{{highlight(d/x=root(3,6/pi))}}}.  Compute this how you want.