A cylindrical bucket holds 44.372 litre of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water level in the tank.

Answer

To find the height of the water level in the rectangular tank after pouring water from the cylindrical bucket, we can follow these steps:

### Step 1: Convert the volume of water from liters to cubic centimeters
We know that 1 liter is equal to 1000 cubic centimeters (cm³). Therefore, we need to convert 44.372 liters into cubic centimeters.

\[ \text{Volume in cm}^3 = 44.372 \, \text{liters} \times 1000 \, \text{cm}^3/\text{liter} = 44372 \, \text{cm}^3 \]

### Step 2: Calculate the volume of the rectangular tank
The volume \( V \) of a rectangular tank can be calculated using the formula:

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

In this case, the length of the tank is 66 cm, the width is 28 cm, and we need to find the height \( h \) of the water level.

### Step 3: Set up the equation for the volume of water in the tank
Since the volume of water in the tank is equal to the volume of water from the bucket, we can set up the equation:

\[ 44372 \, \text{cm}^3 = 66 \, \text{cm} \times 28 \, \text{cm} \times h \]

### Step 4: Calculate the area of the base of the tank
First, we calculate the area of the base of the tank:

\[ \text{Area} = \text{length} \times \text{width} = 66 \, \text{cm} \times 28 \, \text{cm} = 1848 \, \text{cm}^2 \]

### Step 5: Solve for the height \( h \)
Now we can substitute the area into the volume equation and solve for \( h \):

\[ 44372 \, \text{cm}^3 = 1848 \, \text{cm}^2 \times h \]

To find \( h \), we divide both sides by 1848 cm²:

\[ h = \frac{44372 \, \text{cm}^3}{1848 \, \text{cm}^2} \approx 24 \, \text{cm} \]

### Conclusion
The height of the water level in the rectangular tank is approximately **24 cm**.

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