Answer:
The number of passengers that the Embraer E170 could carry if its fuselage was made of steel is 39 passengers
Explanation:
The given parameters of the cylinder representing the fuselage are;
The length of the cylinder, l = 30.0 meters
The width of the cylinder, w = 2.5 meters
The thickness of the cylinder, t = 2.5 mm = 0.0025 meters
The volume of the metal required to make the fuselage cylinder, V = (π·w²/4 - π·(w - 2·t)²/4) × l
Therefore, by substituting the known values, we have;
V = (π × 2.5²/4 - π×(2.5 - 2×0.0025)²/4) × 30 = 0.58845957392
The volume of the metal required to make the fuselage cylinder, V≈ 0.58846m³
The given density of steel = 7.87 g/cm³ = 7870 kg/m³
The given density of aluminum = 2.70 g/cm³ = 2,700 kg/m³
Mass = Density × Volume
The mass of the fuselage made with steel = The given density of steel × The volume of the metal required to make the fuselage cylinder
∴ The mass of the fuselage made with steel = 7870 × 0.58846 ≈ 4631.18
The mass of the fuselage made with steel ≈ 4631.18 kg
Similarly, the mass of the fuselage made with aluminum = 2,700 × 0.58846 ≈ 1588.84
The mass of the fuselage made with aluminum ≈ 1588.84 kg
The total mass the Embraer E170 could carry = The mass of the fuselage made with aluminum + The mass of the 78 passengers
The average mass of each passenger = 79 kg
∴ The total mass the Embraer E170 could carry ≈ 1588.84 + 78 × 79 = 7750.84
The total mass the Embraer E170 could carry ≈ 7750.84 kg
The extra mass the Embraer E170 could carry when made of steel = (The total mass the Embraer E170 can carry) - (The mass of the fuselage made with steel)
∴ The extra mass the Embraer E170 could carry when made of steel = 7750.84 - 4631.18 = 3119.36
The extra mass the Embraer E170 could carry when made of steel ≈ 3119.36 kg
The number of passengers the Embraer E170 could carry when made of steel = (The extra mass the Embraer E170 could carry when made of steel)/(The average mass of one passenger)
∴ The number of passengers the Embraer E170 could carry if its fuselage was made of steel = 3119.36 kg/(79 kg/passenger) ≈ 39.489 passengers
The number of passengers that the Embraer E170 could carry if its fuselage was made of steel ≈ 39 passengers (we round down when counting people which are whole quantities)
