Given L=10.5mm, W=7.2mm, T=5.8mm, M=0.5g, V=0.4cm3 for an agricultural product, calculate its bulk density.

Here is the solution to Question 1d) from the exam paper:

Question 1d)
Given data for an agricultural product material:

• Length ($L$) = $10.5 \text{ mm}$
• Width ($W$) = $7.2 \text{ mm}$
• Thickness ($T$) = $5.8 \text{ mm}$
• Mass ($M$) = $0.5 \text{ g}$
• Volume ($V$) = $0.4 \text{ cm}^3$

Assumptions:

• The given dimensions ($L, W, T$) define the overall envelope volume of the single agricultural product material (i.e., the volume of the smallest rectangular prism enclosing it).
• The given Volume ($V = 0.4 \text{ cm}^3$) represents the true solid volume of the material, excluding any internal voids or air spaces within its envelope.
• The given Mass ($M = 0.5 \text{ g}$) is the mass of this single material.

Step 1: Convert dimensions to centimeters (cm) for consistency.

$$L = 10.5 \text{ mm} = 1.05 \text{ cm}$$ $$W = 7.2 \text{ mm} = 0.72 \text{ cm}$$ $$T = 5.8 \text{ mm} = 0.58 \text{ cm}$$

Step 2: Calculate the envelope volume ($V_{envelope}$) of the particle.
This is the volume of the smallest rectangular prism enclosing the particle.

$$V_{envelope} = L \times W \times T$$ $$V_{envelope} = 1.05 \text{ cm} \times 0.72 \text{ cm} \times 0.58 \text{ cm}$$ $$V_{envelope} = 0.43848 \text{ cm}^3$$