SOLUTION: A 10 by 12 cm 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 cub

Algebra ->  Volume -> SOLUTION: A 10 by 12 cm 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 cub      Log On


   

Question 1149749: A 10 by 12 cm 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 the water in the container?
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.

The side of the cube is  root%283%2C216%29 = 6 cm.


Let h be the water level in the contender originally.

Notice it became 6 cm after the cube was placed in the container.


So, the original water volume in the container was  V%5B1%5D = 10*12*h cm^3.


After placing the cube, the volume of water is  V%5B2%5D = (10*12*6 - 216) cm^3.


Both volumes are the same,  V%5B1%5D = V%5B2%5D,  which gives you an equation for h


    10*12*h = 10*12*6 - 216,   or

    120h    = 504

       h    = 504%2F120 = 42%2F10 = 4.2 cm.    ANSWER

Solved.