A feild is 70 m long and 40 m broad. In one corner of the field, a pit which is 10 m long, 8 m broad and 5 m deep, has been dug out. The earth taken out of it is evenly spread over the remaining part of the field. Find the rise in the level of the field.

Answer

To find the rise in the level of the field after the earth from the pit is spread evenly over the remaining part of the field, we can follow these steps:

### Step 1: Calculate the area of the rectangular field.
The area of the field can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 70 m
- Breadth = 40 m

Calculating the area:
\[ \text{Area} = 70 \, \text{m} \times 40 \, \text{m} = 2800 \, \text{m}^2 \]

### Step 2: Calculate the volume of the pit.
The volume of the pit can be calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Depth} \]
Given:
- Length = 10 m
- Breadth = 8 m
- Depth = 5 m

Calculating the volume:
\[ \text{Volume} = 10 \, \text{m} \times 8 \, \text{m} \times 5 \, \text{m} = 400 \, \text{m}^3 \]

### Step 3: Calculate the area of the pit.
The area of the pit can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Using the same dimensions as above:
\[ \text{Area of the pit} = 10 \, \text{m} \times 8 \, \text{m} = 80 \, \text{m}^2 \]

### Step 4: Calculate the remaining area of the field.
The remaining area of the field after the pit is dug can be calculated as:
\[ \text{Remaining Area} = \text{Total Area} - \text{Area of the Pit} \]
Calculating the remaining area:
\[ \text{Remaining Area} = 2800 \, \text{m}^2 - 80 \, \text{m}^2 = 2720 \, \text{m}^2 \]

### Step 5: Calculate the rise in the level of the field.
Let the rise in the level of the field be \( h \). The volume of earth taken out from the pit is spread over the remaining area, so we can use the formula:
\[ \text{Volume} = \text{Area} \times \text{Height} \]
Thus:
\[ 400 \, \text{m}^3 = 2720 \, \text{m}^2 \times h \]

Now, solving for \( h \):
\[ h = \frac{400 \, \text{m}^3}{2720 \, \text{m}^2} \]
Calculating \( h \):
\[ h = \frac{400}{2720} \approx 0.147 \, \text{m} \]

### Step 6: Convert \( h \) to centimeters.
To convert meters to centimeters, we multiply by 100:
\[ h = 0.147 \, \text{m} \times 100 = 14.7 \, \text{cm} \]

### Final Answer:
The rise in the level of the field is approximately \( 0.147 \, \text{m} \) or \( 14.7 \, \text{cm} \).

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