Question 1129768
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The total volume of the large cylindrical container is  {{{pi*r^2*h}}} = {{{pi*8^2*32}}} = {{{2048*pi}}} cm^3.


The volume of the water in the large container initially is  {{{pi*8^2*26}}} = 1664 cm^3.


The volume of the free space in the large cylinder over the water surface is  {{{2048*pi}}} - {{{1664*pi}}} = {{{384*pi}}} cm^3.


The volume of the smaller cylinder is  {{{pi*5^2*28}}} = {{{700*pi}}} cm^3.


When the smaller cylinder is fully submersed into the water in the larger cylinder, it displaces  

    {{{(700*pi- 384*pi)}}} = {{{316*pi}}} cm^3 of water out from the larger cylinder.



After that, the volume of the water of {{{pi*8^2*(32-28)}}} = {{{256*pi}}} cm^3 will go from the larger cylinder to the smaller one.



Thus, when the smaller cylinder is taken out from the larger, it carries off / (removes) the volume of  

    {{{256*pi}}} of water from the larger cylinder.



Thus, the total volume of water  {{{316*pi}}} + {{{256*pi}}} = {{{572*pi}}} cm^3  went finally out from the larger cylinder.


So, finally the level of remained water in the larger cylinder is  {{{(1664*pi - 572*pi)/(pi*8^2)}}} = {{{(1664-650)/8^2}}} = 17.0625 centimeters.    (*)


            the level of water in the smaller cylinder is  {{{(256*pi)/(pi*5^2)}}} = {{{256/5^2}}} = 10.24 centimeters.    (**)


And the difference of these levels (*) and (**)  is  17.0625 - 10.24 = 6.8225 centimeters.     <U>ANSWER</U>


<U>Answer</U>.  The difference of the levels is 6.8225 centimeters.  Option B).
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Solved and totally completed.