A cube of 11 cm edge is immersed completely in a rectangular vessel container water. If the dimensions of base are 15 cm and 12 cm . Find the rise in water level in the vessel :

Options

A. 6.85 cm
B. 7 cm
C. 7.31 cm
D. 7.39 cm

Answer

To find the rise in water level in the rectangular vessel when a cube of edge length 11 cm is completely immersed in it, we can follow these steps:

### Step 1: Calculate the Volume of the Cube
The formula for the volume \( V \) of a cube with edge length \( a \) is given by:
\[ V = a^3 \]
Given that the edge length \( a = 11 \) cm, we can calculate the volume:
\[ V = 11^3 = 11 \times 11 \times 11 = 1331 \text{ cm}^3 \]

### Step 2: Calculate the Base Area of the Rectangular Vessel
The base area \( A \) of the rectangular vessel can be calculated using the formula:
\[ A = \text{length} \times \text{breadth} \]
Given the dimensions of the base are 15 cm and 12 cm:
\[ A = 15 \times 12 = 180 \text{ cm}^2 \]

### Step 3: Find the Rise in Water Level
The rise in water level \( h \) in the vessel can be found using the formula:
\[ h = \frac{V}{A} \]
Substituting the values we calculated:
\[ h = \frac{1331 \text{ cm}^3}{180 \text{ cm}^2} \]

### Step 4: Perform the Division
Now, we perform the division to find \( h \):
\[ h = \frac{1331}{180} \approx 7.3944 \text{ cm} \]
Rounding to two decimal places, we find:
\[ h \approx 7.39 \text{ cm} \]

### Conclusion
The rise in water level in the vessel is approximately \( 7.39 \) cm.

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