Question 1203306
.
A solid metal sphere is melted and recast into a hollow spherical shell whose outer radius is 20 cm. 
If the radius of the hollow interior of the shell is equal to the radius of the original sphere, 
what is the radius of the original sphere?
~~~~~~~~~~~~~~~~~


<pre>
Let "r" be the radius of the original sphere.


The volume of the outer sphere is  {{{(4/3)*pi*20^3}}} cm^3.

The volume of the interior sphere is {{{(4/3)*pi*r^3}}} cm^3.

The volume of the original sphere is {{{(4/3)*pi*r^3}}} cm^3.


An equation for the metal volume is 

    {{{(4/3)*pi*20^3}}} - {{{(4/3)*pi*r^3}}} = {{{(4/3)*pi*r^3}}}.


Reduce the factor {{{(4/3)*pi}}} in both sides.  You will get this equation

    {{{20^3}}} - {{{r^3}}} = {{{r^3}}}.


Simplify it and find "r"

    8000 = {{{r^3}}} + {{{r^3}}}

    8000 = {{{2r^3}}}

    {{{r^3}}} = 8000/2 = 4000

    r = {{{root(3,4000)}}} = 15.874 cm  (rounded).   <U>ANSWER</U>
</pre>

Solved.