A rectangular field is 112m long and 62m broad. A cubical tank of edge 6m is dug at each of the four corners of the field and the earth so removed is evenly spread on the remaining field. Find the rise in level.

Answer

To solve the problem step by step, let's break it down into manageable parts.

### Step 1: Calculate the Area of the Rectangular Field
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{length} \times \text{breadth} \]
Given:
- Length = 112 m
- Breadth = 62 m

Calculating the area:
\[ A = 112 \, \text{m} \times 62 \, \text{m} = 6944 \, \text{m}^2 \]

### Step 2: Calculate the Volume of Earth Dug Out
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
where \( a \) is the length of the edge of the cube. Given that the edge of the cubical tank is 6 m:
\[ V = 6 \, \text{m} \times 6 \, \text{m} \times 6 \, \text{m} = 216 \, \text{m}^3 \]

Since there are 4 such tanks dug at the corners, the total volume of earth dug out is:
\[ \text{Total Volume} = 4 \times 216 \, \text{m}^3 = 864 \, \text{m}^3 \]

### Step 3: Calculate the Area of the Remaining Field
The area of the four corners dug out is:
\[ \text{Area of one cube} = 6 \, \text{m} \times 6 \, \text{m} = 36 \, \text{m}^2 \]
Thus, the total area of the four corners is:
\[ \text{Total Area of corners} = 4 \times 36 \, \text{m}^2 = 144 \, \text{m}^2 \]

Now, the area of the remaining field is:
\[ \text{Remaining Area} = \text{Total Area} - \text{Area of corners} = 6944 \, \text{m}^2 - 144 \, \text{m}^2 = 6800 \, \text{m}^2 \]

### Step 4: Calculate the Rise in Level
The rise in level \( h \) can be calculated using the formula:
\[ h = \frac{\text{Volume of earth dug out}}{\text{Remaining Area}} \]
Substituting the values:
\[ h = \frac{864 \, \text{m}^3}{6800 \, \text{m}^2} \]

Calculating \( h \):
\[ h = \frac{864}{6800} \approx 0.127 \, \text{m} \]

### Step 5: Convert Rise in Level to Centimeters
To convert meters to centimeters, we multiply by 100:
\[ h = 0.127 \, \text{m} \times 100 = 12.7 \, \text{cm} \]

### Final Answer
The rise in level of the field is approximately **12.7 cm**.

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