The dimensions of a field are `12 m xx 10 m` . A pit 5 m long, 4 m, wide and 2 m deep is dug in one corner of the field and the eartgh removed has been evenly spread overy the remaining area of the field . The level of the field is raised by

Options

A. 30 cm
B. 35 cm
C. 38 cm
D. 40 cm

Answer

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

### Step 1: Calculate the volume of the pit.
The dimensions of the pit are given as:
- Length = 5 m
- Width = 4 m
- Depth = 2 m

The volume \( V \) of the pit can be calculated using the formula for the volume of a rectangular prism:
\[ V = \text{Length} \times \text{Width} \times \text{Depth} \]
Substituting the values:
\[ V = 5 \, \text{m} \times 4 \, \text{m} \times 2 \, \text{m} = 40 \, \text{m}^3 \]

### Step 2: Calculate the area of the field.
The dimensions of the field are:
- Length = 12 m
- Width = 10 m

The area \( A \) of the field can be calculated using the formula for the area of a rectangle:
\[ A = \text{Length} \times \text{Width} \]
Substituting the values:
\[ A = 12 \, \text{m} \times 10 \, \text{m} = 120 \, \text{m}^2 \]

### Step 3: Calculate the area of the pit.
The area of the pit can also be calculated:
\[ \text{Area of the pit} = \text{Length} \times \text{Width} = 5 \, \text{m} \times 4 \, \text{m} = 20 \, \text{m}^2 \]

### Step 4: Calculate the remaining area of the field.
The remaining area of the field after the pit is dug can be calculated as:
\[ \text{Remaining Area} = \text{Total Area} - \text{Area of the pit} \]
Substituting the values:
\[ \text{Remaining Area} = 120 \, \text{m}^2 - 20 \, \text{m}^2 = 100 \, \text{m}^2 \]

### Step 5: Calculate the rise in level of the field.
The volume of the earth removed from the pit (which is 40 m³) is spread evenly over the remaining area (100 m²). The rise in level \( h \) can be calculated using the formula:
\[ h = \frac{\text{Volume}}{\text{Area}} \]
Substituting the values:
\[ h = \frac{40 \, \text{m}^3}{100 \, \text{m}^2} = 0.4 \, \text{m} \]

### Step 6: Convert the rise in level to centimeters.
To convert meters to centimeters, we multiply by 100:
\[ h = 0.4 \, \text{m} \times 100 = 40 \, \text{cm} \]

### Final Answer:
The level of the field is raised by **40 cm**.

---