Step 1: A wind turbine has blade length 40 m (swept area A = πr²) in wind v = 12 m/s (ρ = 1.225 kg/m³). Find the available wind power and a realistic electrical output. Step 2: A = π × 40² = 5027 m². Step 3: P_wind = ½ρAv³ = 0.5 × 1.225 × 5027 × 12³ = 0.5 × 1.225 × 5027 × 1728. Step 4: 0.5 × 1.225 = 0.6125; × 5027 = 3079; × 1728 = 5.32×10⁶ W ≈ 5.3 MW. Step 5: Betz limit caps extraction at 59%: 3.1 MW; real turbines achieve C_p ≈ 0.45 → ~2.4 MW electrical. Result: ~5.3 MW in the wind, ~2.4 MW electricity — the v³ law means 12 m/s wind carries 8× the power of 6 m/s wind.