The length and breadth of a cuboidal pit are 8 m and 6 m respectively. It is dug to the depth of 10 m and the earth removed from it is spread evenly on a square plot of length 40 m. Find thde height of the earth spread on the plot.

Answer

To solve the problem step by step, we will follow the process of calculating the volume of the cuboidal pit and then using that volume to find the height of the earth spread on the square plot.

### Step 1: Calculate the Volume of the Cuboidal Pit
The volume \( V \) of a cuboid is given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
For the given cuboidal pit:
- Length = 8 m
- Breadth = 6 m
- Depth (height of the pit) = 10 m

Now, substituting the values:
\[ V = 8 \, \text{m} \times 6 \, \text{m} \times 10 \, \text{m} = 480 \, \text{m}^3 \]

### Step 2: Determine the Area of the Square Plot
The area \( A \) of a square is given by the formula:
\[ A = \text{side} \times \text{side} \]
For the square plot with a side length of 40 m:
\[ A = 40 \, \text{m} \times 40 \, \text{m} = 1600 \, \text{m}^2 \]

### Step 3: Set Up the Equation for Height of Earth Spread
Let the height of the earth spread on the plot be \( h \). The volume of earth spread on the plot can also be expressed as:
\[ \text{Volume} = \text{Area} \times \text{Height} \]
Thus, we have:
\[ 480 \, \text{m}^3 = 1600 \, \text{m}^2 \times h \]

### Step 4: Solve for Height \( h \)
Rearranging the equation to solve for \( h \):
\[ h = \frac{480 \, \text{m}^3}{1600 \, \text{m}^2} \]
Calculating \( h \):
\[ h = \frac{480}{1600} = 0.3 \, \text{m} \]

### Conclusion
The height of the earth spread on the square plot is \( 0.3 \, \text{m} \).

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