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

Algebra ->  Volume -> 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      Log On


   

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) About Me  (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?
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Let "r" be the radius of the original sphere.


The volume of the outer sphere is  %284%2F3%29%2Api%2A20%5E3 cm^3.

The volume of the interior sphere is %284%2F3%29%2Api%2Ar%5E3 cm^3.

The volume of the original sphere is %284%2F3%29%2Api%2Ar%5E3 cm^3.


An equation for the metal volume is 

    %284%2F3%29%2Api%2A20%5E3 - %284%2F3%29%2Api%2Ar%5E3 = %284%2F3%29%2Api%2Ar%5E3.


Reduce the factor %284%2F3%29%2Api in both sides.  You will get this equation

    20%5E3 - r%5E3 = r%5E3.


Simplify it and find "r"

    8000 = r%5E3 + r%5E3

    8000 = 2r%5E3

    r%5E3 = 8000/2 = 4000

    r = root%283%2C4000%29 = 15.874 cm  (rounded).   ANSWER

Solved.