Question 1106588
A metal sphere of radius 9 is melted and transformed into three identical spheres.
Find the volume of the original sphere
V = {{{4/3}}}{{{pi*9^3}}}
V = 3053.628 cu/cm
then
{{{3053.628/3}}} = 1017.876 cu/cm is the volume of the smaller spheres
:
 What are the radii of these spheres?
{{{4/3}}}{{{pi*r^3}}} = 1017.876
{{{4*pi*r^3}}} = 3(1017.876)
{{{r^3}}} = {{{3053.628/(4*pi)}}}
{{{r^3}}} = 243
r = {{{243^(1/3)}}}
r = 6.24 cm
:
 What is the ratio of the area of one of these spheres to the area of the original sphere?
{{{(4*pi*6.24^2)/(4*pi*9^2)}}}
cancel 4pi
{{{(6.24^2)/(9^2)}}} = {{{38.94/81}}} ~ {{{39/81}}}
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