A rectangular container whose base is a square of side 12 cm, contains sufficient water to submerge a rectangular solid `8 cm xx 6 cm xx 3 cm`. Find the rise in level of the water in the container when the solid is in it.

Answer

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

### Step 1: Calculate the volume of the rectangular solid
The dimensions of the rectangular solid are given as:
- Length = 8 cm
- Width = 6 cm
- Height = 3 cm

The volume \( V \) of the rectangular solid can be calculated using the formula:
\[ V = \text{Length} \times \text{Width} \times \text{Height} \]
Substituting the values:
\[ V = 8 \, \text{cm} \times 6 \, \text{cm} \times 3 \, \text{cm} = 144 \, \text{cm}^3 \]

### Step 2: Calculate the area of the base of the container
The base of the container is a square with a side length of 12 cm. The area \( A \) of the base can be calculated using the formula:
\[ A = \text{Side} \times \text{Side} \]
Substituting the value:
\[ A = 12 \, \text{cm} \times 12 \, \text{cm} = 144 \, \text{cm}^2 \]

### Step 3: Determine the rise in water level
When the rectangular solid is submerged in the water, it will displace an amount of water equal to its volume. The rise in water level \( h \) can be calculated using the formula:
\[ h = \frac{\text{Volume of solid}}{\text{Area of base}} \]
Substituting the values:
\[ h = \frac{144 \, \text{cm}^3}{144 \, \text{cm}^2} = 1 \, \text{cm} \]

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

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