SOLUTION: A solid cube of side 8 cm is dropped into a cylindrical tank of radius 7 cm. Calculate the rise in the water level if the original depth of water was 9 cm

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Question 789073: A solid cube of side 8 cm is dropped into a cylindrical tank of radius 7 cm. Calculate the rise in the water level if the original depth of water was 9 cm
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We have to assume that the cube is dense enough so it will not float, because if it floated we would need to now what fraction of the cube was submerged.

Since the original depth of water, 9 cm, was higher than the height (8 cm) of the cube, the entire cube will be underwater, displacing a volume of water equal to the volume of the cube.
The volume of the cube is
%288cm%29%5E3=512cm%5E3
The water displaced will fill a cylinder of radius 7 cm and height hcm above the previous water level.
The volume of the cylinder of displaced water is
pi%2A%287cm%29%5E2%2Ah=512cm%5E3
h=512%2F%28pi%2A%287cm%29%5E2%29=512%2F49picm=3.3cm(rounded to the nearest millimeter).