In farmstead planning and poultry housing design:

• Statement (I) is false: Open-sided cage houses (battery cages) are predominantly built in warm, tropical, and sub-tropical regions (like India) to maximize natural cross-ventilation and prevent heat stress. In very cold regions, poultry require well-insulated, climate-controlled, closed deep-litter housing rather than drafty open cage systems.
• Statement (II) is true: Poultry cages are fabricated from durable galvanized welded wire mesh with a sloped floor (typically a 1:6 to 1:8 slope) extending forward into an egg collection cradle, allowing newly laid eggs to roll safely out of the bird's reach.

In dairy cattle housing and farmstead engineering:
Pen Barns consist of individual or small-group enclosed pens designed for specialized animal care and isolation:

• Calf pens (B) for newborn calf feeding and rearing.
• Maternity / Calving pens (C) to provide clean, quiet, sanitary conditions during parturition.
• Isolation / Quarantine pens (D) for housing sick or injured animals to prevent disease transmission.

In contrast, lactating cows are milked in a dedicated Milking Parlour (A) or stanchion milking barn, not in general pen barns.

Matching dairy farmstead housing components:
(A) Milking parlour: An integral functional unit of modern loose housing systems (III) where cows move freely from the resting area into the parlour strictly for milking.
(B) Milk colony: Large municipal or state cooperative dairy settlements (e.g., Aarey Milk Colony) organized as a community barn (IV).
(C) Sick animal: Housed individually in isolation pen barns (II) to prevent disease spread and provide medical treatment.
(D) Loafing barn (Loafing area / Paddock): An unpaved or paved open air (I) exercise yard attached to the covered resting shed.

Calculation of Rankine's Lateral Pressure Coefficient:

• Formula: Rankine's active lateral pressure coefficient ($k$) for granular grain stored in a shallow bin is given by:
  $$k = \frac{1 - \sin\phi}{1 + \sin\phi}$$
  where $\phi$ is the internal angle of friction of the stored grain mass.
• Substituting $\phi = 30^\circ$:
  $$\sin(30^\circ) = 0.5$$
  $$k = \frac{1 - 0.5}{1 + 0.5} = \frac{0.5}{1.5} = \frac{1}{3} \approx 0.333$$