Question 953226
Volume of sphere={{{(4/3)(pi)(r^3)}}}
{{{413cm^3=(4/3)(pi)(r^3)}}} Multiply each side by {{{3/((4)(pi))}}}
{{{((413cm^3)(3))/(4(pi))=r^3}}}
{{{(1239cm^3)/12.57=r^3}}} 
{{{98.6=r^3}}} Find the cube root of each side.
4.62cm=r
The cubic box to hold the sphere must have edges=2r (diameter of the sphere)
The volume of the cube ={{{(edge)^3}}}={{{(2r)^3}}}={{{9.24^3cm^3}}}
Volume of cube=789 cm^3
Volume wasted=vol(cube)-vol(sphere)=789cm^3-413cm^3=376cm^3
Percent of cube volume wasted=vol(wasted)/vol(cube)=(376cm^3/789cm^3)(100%)=47.7%