SOLUTION: A large cylindrical container with a height of 32cm and a radius of 8cm has water in it to a depth of 26cm. A smaller cylindrical container with no water in it has a height of 28cm

Algebra ->  Volume -> SOLUTION: A large cylindrical container with a height of 32cm and a radius of 8cm has water in it to a depth of 26cm. A smaller cylindrical container with no water in it has a height of 28cm      Log On


   

Question 1129768: A large cylindrical container with a height of 32cm and a radius of 8cm has water in it to a depth of 26cm. A smaller cylindrical container with no water in it has a height of 28cm and a radius of 5cm. The smaller container container is lowered into the larger. As it is lowered, water rises in the larger and then spills out onto the ground until the top of the smaller container is level with the top of the larger. As the smaller container is lowered further, water from the larger spills into the smaller. When the smaller container is lowered all the way, it is then removed. What is the difference in cm in the height of the water left in the larger container and the height of the water that spilled into the smaller??.
A)5.9325 B)6.8225 C)6.9125 D)7.0425 E)7.1625
Answer by ikleyn(52785) About Me  (Show Source):
You can put this solution on YOUR website!
.
The total volume of the large cylindrical container is  pi%2Ar%5E2%2Ah = pi%2A8%5E2%2A32 = 2048%2Api cm^3.


The volume of the water in the large container initially is  pi%2A8%5E2%2A26 = 1664 cm^3.


The volume of the free space in the large cylinder over the water surface is  2048%2Api - 1664%2Api = 384%2Api cm^3.


The volume of the smaller cylinder is  pi%2A5%5E2%2A28 = 700%2Api cm^3.


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

    %28700%2Api-+384%2Api%29 = 316%2Api cm^3 of water out from the larger cylinder.



After that, the volume of the water of pi%2A8%5E2%2A%2832-28%29 = 256%2Api 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%2Api of water from the larger cylinder.



Thus, the total volume of water  316%2Api + 256%2Api = 572%2Api cm^3  went finally out from the larger cylinder.


So, finally the level of remained water in the larger cylinder is  %281664%2Api+-+572%2Api%29%2F%28pi%2A8%5E2%29 = %281664-650%29%2F8%5E2 = 17.0625 centimeters.    (*)


            the level of water in the smaller cylinder is  %28256%2Api%29%2F%28pi%2A5%5E2%29 = 256%2F5%5E2 = 10.24 centimeters.    (**)


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


Answer.  The difference of the levels is 6.8225 centimeters.  Option B).


Solved and totally completed.