Question

What is the weight of one centimeter of surface soil over one hectare of land?

• A. 100 t
• B. 150 t
• C. 200 t
• D. 250 t

Hint:

Keep this standard conversion factor in mind:
Every \( 1 \text{ cm} \) depth of soil over \( 1 \text{ hectare} \) weighs approximately \( 150 \text{ tons} \).
You can multiply this factor by any target depth (e.g., \( 15 \text{ cm} \text{ furrow slice} = 15 \times 150 = 2250 \text{ t} \)) to quickly estimate soil weights.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
To calculate the weight of a soil layer, we use the relationship between volume, density, and mass.
The dry mass of a given volume of soil is determined by its bulk density.
Key Formula or Approach:
Volume of soil (\( V \)):
\[ V = \text{Area (A)} \times \text{Depth (d)} \]
Mass of soil (\( M \)):
\[ M = \text{Volume (V)} \times \text{Soil Bulk Density } (\rho_b) \]

Step 2: Detailed Explanation:
Let us perform the calculations step-by-step:
Identify the dimensions:
- Area of 1 hectare, \( A = 10,000 \text{ m}^2 \).
- Depth of the soil layer, \( d = 1 \text{ cm} = 0.01 \text{ m} \).
Calculate the volume of soil in this layer:
\[ V = 10,000 \text{ m}^2 \times 0.01 \text{ m} = 100 \text{ m}^3 \]
Determine the bulk density (\( \rho_b \)) of typical agricultural soil:
- The standard average bulk density of mineral surface soil is approximately \( 5 \text{ g/cm}^3 \).
- Convert this bulk density value to tons per cubic meter (\( \text{t/m}^3 \)):
\[ 5 \text{ g/cm}^3 = 1500 \text{ kg/m}^3 = 5 \text{ t/m}^3 \]
Calculate the total mass of the soil layer:
\[ M = V \times \rho_b \]
\[ M = 100 \text{ m}^3 \times 5 \text{ t/m}^3 = 150 \text{ tons (t)} \]
Therefore, the average weight of a 1 cm layer of surface soil over a 1 hectare area is approximately \( 150 \text{ t} \).
- Note: This matches the standard agronomic assumption where a standard furrow slice (approx. \( 15 \text{ cm} \) deep) over one hectare weighs approximately \( 25 \times 10^6 \text{ kg} \) or \( 2250 \text{ t} \) (\( 15 \times 150 \text{ t} = 2250 \text{ t} \)).

Step 3: Final Answer:
The weight of one centimeter of surface soil over one hectare of land is 150 t.