A rectangular water tank of base `11 m xx 6 m` contains water up to a height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 1.75 m, find the height of the water level in the tank.

Answer

To solve the problem, we need to calculate the volume of water in the rectangular tank and then use that volume to find the height of the water level in the cylindrical tank.

### Step 1: Calculate the volume of water in the rectangular tank.

The formula for the volume \( V \) of a rectangular prism (tank) is given by:

\[ V = \text{length} \times \text{width} \times \text{height} \]

For the rectangular tank:
- Length = 11 m
- Width = 6 m
- Height = 5 m

Substituting the values into the formula:

\[ V = 11 \, \text{m} \times 6 \, \text{m} \times 5 \, \text{m} \]

Calculating the volume:

\[ V = 11 \times 6 = 66 \, \text{m}^2 \]
\[ V = 66 \times 5 = 330 \, \text{m}^3 \]

So, the volume of water in the rectangular tank is \( 330 \, \text{m}^3 \).

### Step 2: Calculate the height of the water level in the cylindrical tank.

The formula for the volume \( V \) of a cylinder is given by:

\[ V = \pi r^2 h \]

Where:
- \( r \) is the radius of the base of the cylinder
- \( h \) is the height of the cylinder

We know the volume of water is the same, so we set the volume of the cylindrical tank equal to the volume of water we calculated:

\[ 330 = \pi (1.75)^2 h \]

Calculating \( \pi (1.75)^2 \):

\[ (1.75)^2 = 3.0625 \]
\[ \pi (1.75)^2 \approx 3.14 \times 3.0625 \approx 9.621875 \]

Now substituting back into the equation:

\[ 330 = 9.621875 h \]

To find \( h \), we rearrange the equation:

\[ h = \frac{330}{9.621875} \]

Calculating \( h \):

\[ h \approx 34.3 \, \text{m} \]

### Final Answer:
The height of the water level in the cylindrical tank is approximately \( 34.3 \, \text{m} \).

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