Second moment of area of a hollow circular section Find the moment of inertia about the centroidal axis of a hollow circular section with external diameter 8 cm and internal diameter 6 cm (use standard engineering approximation).

Introduction / Context:The second moment of area (area moment of inertia) about the centroidal axis is fundamental for bending stress and deflection calculations. Circular tubes are common in shafts, columns, and frames, so knowing the formula is essential.

Given Data / Assumptions:

• External diameter D = 8 cm, internal diameter d = 6 cm.
• Centroidal (through the centre) bending axis.
• Use the standard thin/solid ring formula without LaTeX.

Concept / Approach:

The centroidal second moment for a circular annulus is I = (π/64) * (D^4 − d^4). Plug in diameters in consistent units (cm) to get cm^4.

Step-by-Step Solution:

Verification / Alternative check:

Compare with solid circle of D = 8 cm: I_solid = (π/64)4096 ≈ 201.1 cm^4; removing inner core of d = 6 cm removes (π/64)1296 ≈ 63.7 cm^4; difference ≈ 137.4 cm^4, confirming.

Why Other Options Are Wrong:

Other values correspond to incorrect arithmetic or missing π factor; 437.5 cm^4 is roughly 43.7510, not 43.75π.

Common Pitfalls:

Using radii instead of diameters in the D^4 form; mixing units leading to m^4 instead of cm^4.

Final Answer:

137.5 cm^4