SOLUTION: 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

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?
Answer by ikleyn(52817) (Show Source): You can put this solution on YOUR website!
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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?
~~~~~~~~~~~~~~~~~

Let "r" be the radius of the original sphere.


The volume of the outer sphere is   cm^3.

The volume of the interior sphere is  cm^3.

The volume of the original sphere is  cm^3.


An equation for the metal volume is 

     -  = .


Reduce the factor  in both sides.  You will get this equation

     -  = .


Simplify it and find "r"

    8000 =  + 

    8000 = 

     = 8000/2 = 4000

    r =  = 15.874 cm  (rounded).   ANSWER

Solved.

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