SOLUTION: A cube with edge 10ft is submerged in a rectangular tank containing water. If the tank is 40 ff by 50 ft, how much does the level of water in the tank rise? This is the probl

Question 273502: A cube with edge 10ft is submerged in a rectangular tank containing water. If the tank is 40 ff by 50 ft, how much does the level of water in the tank rise?
This is the problem, we have figured the volume of the cube to be 1000 cubic feet - but that is as far as we have gotten.
Any help would be great - Thanks.
Found 2 solutions by josmiceli, ankor@dixie-net.com:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
there are 2 key points in this problem:
(1)
The cube is "submerged" in the tank. That means the cube is made of
granite and not styrofoam.
(2)
The tank has enough water in it to cover the cube, and therefore
submerge it. The height of the water must be higher than 10 ft
when the cube is submerged
----------------------------
I can assume the height of the water in the tank is initially ft
Then the volume of water in the tank is 10 x 40 x 50 = ft3
With the cube in the water, the volume of water + cube in the tank
is ft3
The new height of the water in the tank will be
ft
The water in the tank rises .5 ft
(and it does cover the cube, too. If it didn't, the answer would be wrong)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A cube with edge 10ft is submerged in a rectangular tank containing water.
If the tank is 40 ff by 50 ft, how much does the level of water in the tank rise?
:
Assume the original water level in the tank is 10 feet
Vol = 40 * 50 * 10
Vol = 20,000 cu/ft
You drop in the cube which is 1000 cu/ft
Vol of water now = 21,000
:
Let h = height of the water now
40 * 50 * h = 21000
2000h = 21000
h = 21000/2000
h = 10.5 ft is height of the water now
therefore
10.5 - 10 = .5 ft rise when you add 1000 cu/ft
;
:
Prove that: find the water volume of 40 * 50 * .5 = 1000 cu/ft
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