SOLUTION: A heavy cube of side 8cm is placed vertically in a cylindrical tank of radius 7cm which contains water. Calculate the rise in the water level if the original depth of water was:

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Question 1205029: A heavy cube of side 8cm is placed vertically in a cylindrical tank of radius 7cm which contains water.
Calculate the rise in the water level if the original depth of water was:
a) 10 cm
b) 2 cm
Found 3 solutions by mananth, ikleyn, n2:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
heavy cube of side 8cm is placed vertically in a cylindrical tank of radius 7cm which contains water.
Calculate the rise in the water level if the original depth of water was:
a) 10cm
b) 2cm
If the height of water is above length of cube then increase in height will be same for any height of water.
Volume of cube = l^3 = 8^3= 512 cm^3
Volume of cylinder per cm height = pi*7^2 = 49 *pi
Increase in height = 512/(49*pi) = 3.326 cm
When the height of water is 2 cm
The cube will sink only 2 cm in height
Volume of sunk portion = 8*8*2=128 cm^3
Increase in height = 128/949*pi) =0.424 cm
you round it off as desired or convert to fraction

Answer by ikleyn(53575)   (Show Source):
You can put this solution on YOUR website!
.
A heavy cube of side 8cm is placed vertically in a cylindrical tank of radius 7cm which contains water.
Calculate the rise in the water level if the original depth of water was:
a) 10cm
b) 2cm
~~~~~~~~~~~~~~~~~

        Regarding this problem and its solution in the post by @mananth, I'd like to make two notices.

        First notice to (1) is that the solution by @mananth is correct ONLY IF the cylindrical tank
        has enough height in order for the displaced water does not flow out of the cylinder.
        Otherwise, the rise in the water level will be limited by the height of the cylinder.
        The problem says nothing about it, and it is the problem's FAULT.

        Second notice is that the solution by @mananth for part 2) is FATALLY INCORRECT.
        See my correct solution below.

                                Solution to part 2

The original volume of the water in the tank is = = 307.87582 cm^3. The area of the horizontal section of the tank, occupied by the water after placing the solid cube is = = 89.93791 cm^2. The final level of the water is then = 3.423204075 cm, or 3.423 cm after rounding. Thus the rise of the water level is the difference 3.423 - 2 = 1.423 cm.

Solved correctly.

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Again, the solution by @mananth for part 2) is CONCEPTUALLY INCORRECT,
since he/she incorrectly determines the volume of the displaced water,
which is of fundamental importance in this problem.

Answer by n2(49)   (Show Source):
You can put this solution on YOUR website!
.
A heavy cube of side 8 cm is placed vertically in a cylindrical tank of radius 7 cm which contains water.
Calculate the rise in the water level if the original depth of water was:
    (a)   10 cm
    (b)   2 cm
~~~~~~~~~~~~~~~~~~~~~~~~~~~

(a) In this case, the entire cube is wholly submerged into the water in the tank. The water level rises over the entire base area of the cylindrical tank. The raised water represents the volume of the displaced water in the tank by the solid cube. Use the law of the volume of water conservation. To find the rise for question (a), we should divide the volume of the cube, cm^3 by the area of the base of the cylinder the rise = = = 3.326 cm. ANSWER to question (a). The rise of the water level is 3.326 cm. (b) In this case, the cube is only partly submerged into the water in the tank. The water level rises over the part of the base area of the cylindrical tank. This part of the area where the water rises is the entire area of the base of the tank minus the area of the base of the cube, which is only partially submerged. Use the law of the volume of water conservation. To find the new level of water for question (b), we should divide the volume of the water in the tank, which is cm^3, by the (area of the tank base MINUS area of the cube base) the new level = = 3.4232 cm (rounded). Thus the raise of the water level is 3.4232 - 2 = 1.4232 centimeters. The new level is still lower than the height of the cube, so our calculations make sense. ANSWER to question (b). The rise of the water level is 3.4232 cm.

Solved.