A tank 40 m long, 30 m broad and 12 m deep is dug in a field 1000 m long and 30 m wide. By how much will the level of the field rise if the earth dug out of the tank is evenly spread over the field ?

Options

A. a)2 metre
B. b)1.2 metre
C. c)0.5 metre
D. d)5 metre

Answer

To solve the problem, we need to determine how much the level of the field will rise when the earth dug out from the tank is spread evenly over the field.

### Step-by-Step Solution:

1. **Calculate the volume of the tank**:
The volume of the tank can be calculated using the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Depth} \]
Given:
- Length = 40 m
- Breadth = 30 m
- Depth = 12 m

\[ \text{Volume} = 40 \, \text{m} \times 30 \, \text{m} \times 12 \, \text{m} = 14400 \, \text{m}^3 \]

2. **Calculate the area of the field**:
The area of the field can be calculated using the formula for the area of a rectangle:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 1000 m
- Breadth = 30 m

\[ \text{Area} = 1000 \, \text{m} \times 30 \, \text{m} = 30000 \, \text{m}^2 \]

3. **Determine the rise in the level of the field**:
To find the rise in the level of the field, we need to divide the volume of the earth dug out from the tank by the area of the field:
\[ \text{Rise in level} = \frac{\text{Volume of earth}}{\text{Area of field}} \]
Substituting the values we calculated:
\[ \text{Rise in level} = \frac{14400 \, \text{m}^3}{30000 \, \text{m}^2} \]

Simplifying this:
\[ \text{Rise in level} = 0.48 \, \text{m} \]

To express this in meters:
\[ \text{Rise in level} = 0.48 \, \text{m} \approx 0.5 \, \text{m} \]

### Final Answer:
The level of the field will rise by approximately **0.5 meters**.