Question 1103372: a 10cm by 12cm rectangular container contains some water. When a solid metal cube with volume 216 cm3 is placed in the water, the water level comes up level with the top of the cube. In cm, what was the original height of of the water in the container
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source):
Answer by ikleyn(52781)  (Show Source):
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a 10cm by 12cm rectangular container contains some water. When a solid metal cube with volume 216 cm3 is placed in the water,
the water level comes up level with the top of the cube. In cm, what was the original height of of the water in the container
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Let H be the level of the water in the container initially, in centimeters, cm.
(It is "the original height of of the water in the container", which is under the question).
Then the volume of water is V = 10*12*H cubic centimeters.
The cube immersed in the water has the edge length of  = 6 cm.
After immersing, the water level in container is exactly 6 cm, according to the condition.
The "volume equation" is
10*12*H + 216 = 10*12*6,
which implies
10*12*H = 10*12*6 - 216 = 504 ====> H =  = 4.2 cm.
Answer. The original height of of the water in the container was 4.2 cm.
Solved.
To see other similar solved problems, look into the lesson
- Water level rise in a tank after submerging bodies
in this site.
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