SOLUTION: A cubic tank of side 36cm is half-filled with water. How much will the water level rise when a metal block of volume 5184cm is placed in the tank?

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Question 1036906: A cubic tank of side 36cm is half-filled with water. How much will the water level rise
when a metal block of volume 5184cm is placed in the tank?
Found 2 solutions by addingup, ikleyn:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
36^3 = 46656 is the volume of the cube
1/2 filled with water:
1/2*46656 = 23328
add a block 5184:
23328+5184 = 28512
What is 28512 of 46656?
28512/46656 = 0.6111...
When you add the metal block the cube will be 61.11% full and:
36*.6111 = 22 cm high, the cube will be filled to the 22 cm mark

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
A cubic tank of side 36 cm is half-filled with water. How much will the water level rise
when a metal block of volume 5184 highlight%28cross%28cm%29%29 cm%5E3 is highlight%28cross%28placed%29%29 submerged in the tank?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

The original volume of the water in the tank is 

V%5B0%5D = 36%5E3%2F2 cm%5E3.   (1)


Let the new level of water after submerging the block be h cm (now unknown).

Since the water volume didn't change, we have this equation:

V%5B0%5D = 36%5E2%2Ah+-+5184,   or, substituting (1),

36%5E3%2F2 = 36%5E2%2Ah+-+5184.

Hence,

h = 36%2F2 + %285184%2F36%5E2%29 = 18 + 4 = 22 cm.

Answer.  Water level in the tank after submerging the block is 22 cm.


Notice.

The term "submerged" means that the block is fully covered by the liquid.