Question

How many kilograms of soil are in one hectare in 15 cm depth having a bulk density of 1.33 g/cm\(^3\)?

• A. 17,95,000 kg
• B. 19,95,000 kg
• C. 15,95,000 kg
• D. 21,95,000 kg

Hint:

For standard agricultural calculations, an acre furrow slice (6 inches deep) weighs approximately 2 million pounds, and a hectare furrow slice (15 cm deep) with a standard bulk density of $1.33\text{ g/cm}^3$ weighs almost exactly 2 million kilograms (specifically $1.995 \times 10^6\text{ kg}$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
To find the mass of soil in a given area and depth, we use the soil bulk density and calculate the total volume of the soil slice.
The relationship is given by:
\[ \text{Mass} = \text{Volume} \times \text{Bulk Density} \]
Key Formula or Approach:
1. Find the volume of soil (\( V \)) in cubic meters (\( \text{m}^3 \)):
\[ V = \text{Area} \times \text{Depth} \]
where Area of 1 hectare = \( 10000\text{ m}^2 \), and Depth = \( 15\text{ cm} = 0.15\text{ m} \).
2. Convert Bulk Density (\( \text{BD} \)) from \( \text{g/cm}^3 \) to \( \text{kg/m}^3 \):
\[ 1\text{ g/cm}^3 = 1000\text{ kg/m}^3 \]
3. Calculate the total mass of the soil slice:
\[ \text{Mass (kg)} = V (\text{m}^3) \times \text{BD} (\text{kg/m}^3) \]

Step 2: Detailed Explanation:
Let us carry out the calculation:
1. Calculate the volume of the soil slice:
\[ V = 10000\text{ m}^2 \times 0.15\text{ m} = 1500\text{ m}^3 \]
2. Convert Bulk Density:
\[ \text{BD} = 1.33\text{ g/cm}^3 = 1.33 \times 1000 = 1330\text{ kg/m}^3 \]
3. Calculate the mass of the soil:
\[ \text{Mass} = 1500\text{ m}^3 \times 1330\text{ kg/m}^3 = 1,995,000\text{ kg} \]
This calculated mass corresponds to the value of \( 19,95,000\text{ kg} \).

Step 3: Final Answer:
The total mass of the soil is 19,95,000 kg, which corresponds to option (B).