A rectangular container has base is a square of side 12 cm . Contains sufficient water to submerge a rectangular solid ` 8 cm xx 6 cm xx 3cm.` find the rise in level of the water in the container when the solid is completely immersed in it.

Answer

To find the rise in the level of water in the container when the rectangular solid is completely immersed, we can follow these steps:

### Step 1: Calculate the Volume of the Rectangular Solid
The volume \( V_s \) of a rectangular solid can be calculated using the formula:
\[ V_s = \text{length} \times \text{breadth} \times \text{height} \]
For the given dimensions of the solid (8 cm, 6 cm, 3 cm):
\[ V_s = 8 \, \text{cm} \times 6 \, \text{cm} \times 3 \, \text{cm} = 144 \, \text{cm}^3 \]

### Step 2: Calculate the Area of the Base of the Container
Since the base of the container is a square with a side of 12 cm, the area \( A \) of the base can be calculated as:
\[ A = \text{side}^2 = 12 \, \text{cm} \times 12 \, \text{cm} = 144 \, \text{cm}^2 \]

### Step 3: Relate the Volume of Water Displaced to the Rise in Water Level
When the solid is immersed in the water, it will displace an amount of water equal to its volume. The rise in water level \( \Delta h \) can be calculated using the formula:
\[ V_s = A \times \Delta h \]
Rearranging this gives us:
\[ \Delta h = \frac{V_s}{A} \]

### Step 4: Substitute the Values
Now substituting the values we calculated:
\[ \Delta h = \frac{144 \, \text{cm}^3}{144 \, \text{cm}^2} = 1 \, \text{cm} \]

### Conclusion
The rise in the level of water in the container when the solid is completely immersed is:
\[ \Delta h = 1 \, \text{cm} \]

---