modern commercial airlines are largely made of aluminum, and light and strong metal. But the fact that aluminum is cheap enough that airplanes can be made out of it is a bit of historical luck. before the discovery of the Hall-Heroult process in 1886, aluminum was as rare and expensive as gold. What would happen if airplanes had to be made of steel? The fuselage of a Boeing 787, which can carry 400 passengers, is approximately a hollow aluminum cylinder without ends, 70.7 m long, 6.5 m wide, and 2.5 mm thick. Suppose this fuselage was made of steel (density 7.87 g/cm^{3}) instead of aluminum (density 2.7g/[tex]cm^{3}), and let's say the average passenger has a mass of 81 kg. We'll also assume the engines can't lift any greater mass than they already do. Calculate the number of passengers that the Boeing 747 could carry if its fuselage was made of steel.

170 passenger .  ( approx )

Explanation:

Total volume of metal making fuselage = π ( r₂² - r₁² ) l

r₂ is outer radius of cylindrical tube like fuselage

= 6.5 / 2 + .0025 = 3.2525 m

r₁ is inner  radius of cylindrical tube like fuselage

= 6.5 / 2 = 3.25 m

l = 70.7 m

Total volume of fuselage = π ( r₂² - r₁² ) l

= 3.14 x 70.7 x ( 3.2525² - 3.25² )

= 221.998 ( 10.57875 - 10.5625)

= 3.60747 m³

If it is made of aluminium , its mass

= volume x density

= 3.60747 x 2700 kg

= 9740.16 kg

weight of passenger = 81 x 400 = 32400 kg

Total mass =  32400 + 9740.16

= 42140.16 kg

If it is made of iron  , its mass

= volume x density

= 3.60747 x 7870 kg

= 28390.79  kg

If number of passenger required be n

81 n + 28390.79 = 42140.16 ( as per condition given )

n = 170 passenger .  ( approx )

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