For a thin-walled cylindrical tank subjected to internal liquid pressure, identify the correct statements about hoop strain, longitudinal strain, and volumetric change of the cylinder.

Introduction / Context:
When a thin-walled cylindrical vessel is subjected to internal liquid pressure, it develops circumferential (hoop) and longitudinal stresses. These lead to corresponding strains and an overall change in volume. This question checks conceptual understanding of the deformation components under thin-cylinder theory.

Given Data / Assumptions:

• Thin-walled cylinder, wall thickness t is small compared to diameter.
• Internal pressure p produces hoop stress σ_h and longitudinal stress σ_l.
• Material is linearly elastic with Young's modulus E and Poisson's ratio ν.

Concept / Approach:
Under thin-cylinder theory, σ_h = pD / (2t) and σ_l = pD / (4t). Strains arise as ε_h = (σ_h / E) − ν (σ_l / E) and ε_l = (σ_l / E) − ν (σ_h / E). Both are non-zero, causing increases in circumference and length. Consequently, the internal volume changes due to these dimensional increases.

Step-by-Step Solution:
1) Recognize two principal stresses: hoop and longitudinal.2) Compute corresponding strains using linear elasticity and Poisson effect.3) Non-zero ε_h implies circumferential expansion (hoop strain).4) Non-zero ε_l implies axial elongation (longitudinal strain).5) Combined dimensional changes imply volumetric change of the cylinder.

Verification / Alternative check:
For p > 0, both σ_h and σ_l are positive, so both ε_h and ε_l are positive for typical ν (0 < ν < 0.5), confirming expansion in both directions and a corresponding volume increase.

Why Other Options Are Wrong:

• Each of A, B, and C captures a real effect; excluding any one would give an incomplete picture.

Common Pitfalls:

• Assuming only hoop effects are present and neglecting longitudinal strain.
• Ignoring Poisson's coupling between orthogonal directions.

Final Answer:
All the above.