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 solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the area of the field
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

Given:
- Length of the field = 70 m
- Breadth of the field = 40 m

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

### Step 2: Calculate the volume of the pit
The volume of a rectangular prism (pit) is given by the formula:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]

Given:
- Length of the pit = 10 m
- Breadth of the pit = 8 m
- Depth of the pit = 5 m

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

### Step 3: Calculate the area of the remaining field
The area of the remaining part of the field can be calculated by subtracting the area of the pit from the total area of the field.

The area of the pit:
\[ \text{Area of the pit} = 10 \, \text{m} \times 8 \, \text{m} = 80 \, \text{m}^2 \]

Calculating the remaining area:
\[ \text{Remaining area} = \text{Total area} - \text{Area of the pit} = 2800 \, \text{m}^2 - 80 \, \text{m}^2 = 2720 \, \text{m}^2 \]

### Step 4: Calculate the rise in the level of the field
Let \( H \) be the rise in the level of the field. The volume of earth taken out from the pit is spread evenly over the remaining area of the field.

The volume of the earth spread over the remaining area can be expressed as:
\[ \text{Volume} = \text{Remaining area} \times H \]
Setting the volume of the pit equal to the volume of the spread earth:
\[ 400 \, \text{m}^3 = 2720 \, \text{m}^2 \times H \]

Solving for \( H \):
\[ H = \frac{400}{2720} \]
\[ H = \frac{5}{34} \, \text{m} \]

### Step 5: Convert the rise in height to centimeters
To convert meters to centimeters:
\[ H = \frac{5}{34} \, \text{m} \times 100 \, \text{cm/m} = \frac{500}{34} \, \text{cm} \approx 14.7 \, \text{cm} \]

### Final Answer
The rise in the level of the field is approximately **14.7 cm**.

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