Question 834571
 A solid sphere of radius 3 cm just fits inside
a hollow cone of radius 6cm and height 8cm. 
:
{{{((4/3)*pi*r^3)/((1/3)*pi*r^2*h)}}}
Using the given values
{{{((4/3)*pi*3^3)/((1/3)*pi*6^2*8)}}} = {{{((4/3)*pi*27)/((1/3)*pi*288)}}}
cancel pi; do the math, reduce the fraction
{{{((4/3)*27)/((1/3)*288)}}} = {{{36/96}}} = {{{3/8}}} fraction of the cone occupied by the sphere