Question

John had a container measuring 35cm by 20cm by 25cm. He placed a solid made of 4 identical 5-cm cubes in the tank and then filled the tank completely with water. He then poured out 11387.5ml of water. What was the height of the water in the tank in the end?

Answer 1

See the diagram.

There are different structures possible with 4 identical cubes of 5cm side.

Base area of the container = 35 x 20 = 700 cm²
Internal volume of the container= 700 x 25 = 17,500 cm³
Volume of the solid = 4 * 5 x 5 x 5 = 500 cm³

The solid of 4 cubes gets immersed completely in water when the container is fully filled.
Amount of water in the container = 17, 500 - 500 = 17, 000 cm³
Volume of water poured out = 11, 387.50 cm³
Water remaining inside = 5, 612.50 cm³

Now the height of water in the container tank depends on the structure of solid and how it is placed (vertical or horizontal).

1.  For solid 1 as in the picture:
     The solid is completely immersed.  
   Volume of water + volume of solid = 6, 112.50 cm³
    Height of water in container = 6,112.50/700 = 8.72 cm
        as the height is > 5 cm, all the solid is completely immersed.

2.  For solid 2 as in the picture:
     The solid is perhaps not completely immersed.
     base area available for water to fill = 700 - 50 cm² = 650 cm²
     Height of water = 6,112.50 / 650 = 8.63 cm
        (as it is < 10 cm, the solid is not completely immersed)

3.  For solid 3 , 4 tier standing.
       base area available for filling water = 700 - 25 cm² = 675 cm²
       height of water = 6,112.50 / 675 = 8.31 cm
       As the height < 20 cm, the solid is not completely immersed.