A solid cube of side 8 cm is dropped into a rectangular container of length 16 cm, breadth 8 cm and height 15 cm which is partly filled with water. If the cube is completely submerged, then the rise of water level (in cm) is:

Correct Answer: The rise of water level is 4 cm (Option 4).

Step-by-Step Explanation:

To find the rise in the water level when the cube is dropped into the container, we use Archimedes' principle, which states that the volume of water displaced by a completely submerged solid object is equal to the volume of the object itself.

Step 1: Calculate the volume of the solid cube.
The formula for the volume of a cube is:
$\text{Volume of cube}={\text{side}}^3$
Given that the side of the cube is 8 cm:
$\text{Volume of cube}=8^3=8\times 8\times 8=512{\text{cm}}^3$

Step 2: Relate the volume of the cube to the displaced water.
Let the rise of the water level in the rectangular container be $h$ cm.
The shape of the displaced water is a rectangular cuboid with the same length and breadth as the container, and a height equal to the rise in water level ($h$).
Given dimensions of the container:
Length ($l$) = 16 cm
Breadth ($b$) = 8 cm

The volume of the displaced water is:
$\text{Volume of displaced water}=\text{length}\times \text{breadth}\times \text{rise of height}$
$\text{Volume of displaced water}=16\times 8\times h=128h{\text{cm}}^3$

Step 3: Solve for the rise of water level ($h$).
Since the cube is completely submerged, we set the volume of the displaced water equal to the volume of the cube:
$128h=512$
Divide both sides by 128:
$h=\frac{512}{128}$
$h=4\text{cm}$

Therefore, the rise of the water level in the container is 4 cm.