SOLUTION: A tank with diameter 44x35x22 has water filled upto 17 cm. A metal sphere is immersed in the tank and 231 cm cube water overflows. What is the radius of the sphere

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Question 1024263: A tank with diameter 44x35x22 has water filled upto 17 cm. A metal sphere is immersed in the tank and 231 cm cube water overflows. What is the radius of the sphere

Answer by ikleyn(52788) About Me  (Show Source):
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A tank with highlight%28cross%28diameter%29%29 dimensions 44x35x22 has water filled upto 17 cm.
A metal sphere is immersed in the tank and 231 cm cube water overflows. What is the radius of the sphere
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0. It was not said directly and explicitly, but it is assumed implicitly that     
   a) the sphere has the diameter less than 22 cm,  and 
   b) finally, the sphere is fully covered by the water.

   It is what the words "the sphere is immersed" mean.


1. V%5B17%5D = 44*35*17 = 26180 cm%5E3 is the volume of water in the tank, when it is filled till 17 cm.


2. The full capacity of the tank is

    V = 44*35*22 = 33880 cm%5E3


3. The equation for the sphere volume is 

   V%5Bsphere%5D = %28V+-+V%5B17%5D%29 + 231.

   Or for the radius R

   %284%2F3%29%2Api%2AR%5E3 = %28V+-+V%5B17%5D%29 + 231.


4. Make calculations and solve for R.