A field is 80 m long and 50 m broad. In one corner of the field, a pit which is 10 m long, 7.5 m broad and 8 m deep has been dug out. The earth taken out of it is evelny 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 the field can be calculated using the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

Given:
- Length of the field = 80 m
- Breadth of the field = 50 m

Calculating the area:
\[ \text{Area of the field} = 80 \, \text{m} \times 50 \, \text{m} = 4000 \, \text{m}^2 \]

### 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 of the pit = 10 m
- Breadth of the pit = 7.5 m
- Depth of the pit = 8 m

Calculating the volume:
\[ \text{Volume of the pit} = 10 \, \text{m} \times 7.5 \, \text{m} \times 8 \, \text{m} = 600 \, \text{m}^3 \]

### Step 3: Calculate the area of the pit
The area of the pit can be calculated using the same formula for area:
\[ \text{Area of the pit} = \text{Length} \times \text{Breadth} \]

Calculating the area:
\[ \text{Area of the pit} = 10 \, \text{m} \times 7.5 \, \text{m} = 75 \, \text{m}^2 \]

### Step 4: Calculate the remaining area of the field
To find the remaining area of the field after the pit is dug, we subtract the area of the pit from the total area of the field:
\[ \text{Remaining Area} = \text{Total Area} - \text{Area of the pit} \]

Calculating the remaining area:
\[ \text{Remaining Area} = 4000 \, \text{m}^2 - 75 \, \text{m}^2 = 3925 \, \text{m}^2 \]

### Step 5: Calculate the rise in the level of the field
The rise in the level of the field can be calculated by dividing the volume of the earth taken out by the remaining area of the field:
\[ \text{Rise in level} = \frac{\text{Volume of the pit}}{\text{Remaining Area}} \]

Calculating the rise:
\[ \text{Rise in level} = \frac{600 \, \text{m}^3}{3925 \, \text{m}^2} \approx 0.1528 \, \text{m} \]

### Step 6: Convert rise in level to centimeters
To convert meters to centimeters, we multiply by 100:
\[ \text{Rise in level in cm} = 0.1528 \, \text{m} \times 100 = 15.28 \, \text{cm} \]

### Final Answer
The rise in the level of the field is approximately **15.28 cm**.

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