A rectangular piece of iron measuring 4 cm by 3 cm at 20 ^o C is heated until its temperature increases by 100…

Analyze the question: A rectangular iron plate of 4 cm × 3 cm is heated through a temperature rise of 100 K (the "100 C" is a change, so Δθ = 100 K). We need the new area using the linear expansivity.

Concept: For area (superficial) expansion, the area expansivity is about twice the linear expansivity:

β = 2α

ΔA = A₀ β Δθ, so A = A₀(1 + βΔθ)

(Note: the options show "cm³", but area should be in cm². This is a typo in the question.)

Solution:

• A₀ = 4 × 3 = 12 cm²
• α = 1.2 × 10⁻⁵ K⁻¹, so β = 2.4 × 10⁻⁵ K⁻¹
• Δθ = 100 K

ΔA = 12 × 2.4 × 10⁻⁵ × 100 ΔA = 12 × 2.4 × 10⁻³ ΔA = 0.0288 cm²

New area = 12 + 0.0288 = 12.0288 cm²

Check with the exact method: Each side expands by a factor (1 + 0.0012): (4.0048)(3.0036) = 12.02882... ≈ 12.0288 cm², which agrees with the result above.

Tip: Remember the pattern: linear α, area 2α, volume 3α. Also, a temperature change in °C equals the same change in K, so the starting temperature of 20°C is just extra information you don't need. Watch for such distractors in WASSCE questions.