To determine the volume of airspace in the soil sample, we need to understand the relationship between the volumes of dry soil, water, and the total volume of the soil-water mixture. Let's break down the problem step-by-step.
Step 1: Understand the Given Information
We have the following data:
- Volume of dry soil (V_dry) = 52 cm³
- Volume of water (V_water) = 48 cm³
- Volume of soil and water (V_total) = 78 cm³
Step 2: Calculate the Volume of Airspace
The volume of airspace in the soil can be calculated using the formula:
[
\text{Volume of airspace} = \text{Total volume} - (\text{Volume of dry soil} + \text{Volume of water})
]
Step 3: Substitute the Values
Now, we can substitute the values we have into the formula:
[
\text{Volume of airspace} = V_total - (V_dry + V_water)
]
Calculating the sum of the volume of dry soil and the volume of water:
[
V_dry + V_water = 52 \, \text{cm}^3 + 48 \, \text{cm}^3 = 100 \, \text{cm}^3
]
Now, substituting this back into the airspace formula:
[
\text{Volume of airspace} = 78 \, \text{cm}^3 - 100 \, \text{cm}^3
]
Step 4: Perform the Calculation
Now we perform the subtraction:
[
\text{Volume of airspace} = 78 \, \text{cm}^3 - 100 \, \text{cm}^3 = -22 \, \text{cm}^3
]
Step 5: Analyze the Result
The negative result indicates that there is an inconsistency in the data provided. The total volume of the soil and water (78 cm³) cannot be less than the combined volume of the dry soil and water (100 cm³). This suggests that the airspace volume cannot be negative, which means that the data might be incorrect or misinterpreted.
Step 6: Conclusion
Given the calculations, the volume of airspace cannot be determined accurately with the provided data. However, if we were to assume that the total volume should be greater than the sum of the dry soil and water, we would need to re-evaluate the data.
Summary of Options
- A. 22 cm³: Incorrect based on calculations.
- B. 26 cm³: Incorrect based on calculations.
- C. 30 cm³: Incorrect based on calculations.
- D. 100 cm³: Incorrect based on calculations.
Revision Summary
- The volume of airspace is calculated by subtracting the sum of the dry soil and water volumes from the total volume.
- A negative airspace volume indicates an inconsistency in the data.
- Always ensure that the total volume is greater than the sum of the individual components (dry soil + water).
- Review the data provided for accuracy before performing calculations.
In this case, none of the options provided are correct based on the calculations performed.