A rectangular tank of dimensions ` 24 m x 12 m xx 8 m ` is dug inside a rectangular field 600 m long and 200 m broad . The earth taken out is evenly spread over the field. By how much will the level of the field rise ?

Options

A. 1.925 cm
B. 0.02 m
C. 0.2 cm
D. none of these

Answer

To solve the problem step by step, we will calculate the volume of the earth dug out from the tank and then determine how much the level of the field will rise when this volume is spread evenly over the field.

### Step 1: Calculate the volume of the rectangular tank.
The volume \( V \) of a rectangular tank can be calculated using the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given the dimensions of the tank are \( 24 \, m \times 12 \, m \times 8 \, m \):
\[ V = 24 \, m \times 12 \, m \times 8 \, m = 2304 \, m^3 \]

### Step 2: Calculate the area of the rectangular field.
The area \( A \) of a rectangular field can be calculated using the formula:
\[ A = \text{length} \times \text{breadth} \]
Given the dimensions of the field are \( 600 \, m \times 200 \, m \):
\[ A = 600 \, m \times 200 \, m = 120000 \, m^2 \]

### Step 3: Calculate the rise in the level of the field.
When the earth dug out from the tank is spread over the field, the rise in the level of the field can be calculated using the formula:
\[ \text{Rise} = \frac{\text{Volume of earth}}{\text{Area of field}} \]
Substituting the values we calculated:
\[ \text{Rise} = \frac{2304 \, m^3}{120000 \, m^2} = 0.0192 \, m \]

### Step 4: Convert the rise into centimeters.
To convert meters to centimeters, we multiply by 100:
\[ 0.0192 \, m \times 100 = 1.92 \, cm \]

### Final Answer
Thus, the level of the field will rise by approximately \( 1.92 \, cm \).

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