Question

A soil sample collected with a cylindrical core sampler having height of 15 cm and diameter of 6 cm has a fresh weight of 500 g and oven dry weight of 450 g. Calculate bulk density

• A. 1.38
• B. 1.17
• C. 1.06
• D. 1.25

Hint:

Always use the oven-dry weight of the soil, not the fresh weight, to calculate bulk density.
Ensure core volume calculations are carried out using the radius ($r = d/2$) in the cylinder volume formula: $V = \pi r^2 h$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Soil bulk density ($BD$) is defined as the dry mass of soil divided by its total volume (including both solid particles and pore space).
It is typically expressed in grams per cubic centimeter ($\text{g cm}^{-3}$).
Key Formula or Approach:
The formula for bulk density is:
\[ BD = \frac{\text{Mass of oven-dry soil } (M_d)}{\text{Total volume of soil cylinder } (V)} \]
The volume of a cylindrical core sampler is calculated as:
\[ V = \pi r^2 h = \pi \left(\frac{d}{2}\right)^2 h \]
where $r$ is the radius, $d$ is the diameter, and $h$ is the height of the cylinder.

Step 2: Detailed Explanation:
Given values from the problem:
Diameter of core, $d = 6\text{ cm} \Rightarrow \text{Radius } r = 3\text{ cm}$.
Height of core, $h = 15\text{ cm}$.
Oven-dry mass of soil, $M_d = 450\text{ g}$ (the fresh weight of $500\text{ g}$ is not used for bulk density calculations).
First, calculate the volume of the cylindrical core sampler ($V$):
\[ V = \pi \times r^2 \times h \]
\[ V = 3.14159 \times (3\text{ cm})^2 \times 15\text{ cm} \]
\[ V = 3.14159 \times 9\text{ cm}^2 \times 15\text{ cm} \]
\[ V = 3.14159 \times 135\text{ cm}^3 \]
\[ V \approx 4115\text{ cm}^3 \]
Next, calculate the soil bulk density ($BD$):
\[ BD = \frac{M_d}{V} \]
\[ BD = \frac{450\text{ g}}{4115\text{ cm}^3} \]
\[ BD \approx 1.061\text{ g cm}^{-3} \]
This value matches the option $1.06\text{ g cm}^{-3}$.

Step 3: Final Answer:
The bulk density of the soil sample is $1.06\text{ g cm}^{-3}$, which corresponds to Option (C).