Question 433394
First find the volume of the rectangular prism:
{{{V = L*W*H}}}
now set this equal to the volume of the sphere:
{{{V = (4/3)(pi)R^3}}} to get:
{{{L*W*H = (4/3)(pi)R^3}}} Solve this for {{{R^3}}}.
{{{R^3 = 3L*W*H/4(pi)}}} Take the cube root of both sides.
{{{R = ((3L*W*H)/4(pi))^(1/3)}}} Now multiply by 2 to get the diameter.
{{{D = 2((3L*W*H)/4(pi))^(1/3)}}} Simplify.
{{{D = ((6L*W*H)/(pi))^(1/3)}}}