Iron density

Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.

Correct result:

m = 15.1437 kg

Solution:

D_{1} = 10 cm h = 3 mm \to cm = 3 / 10 cm = 0.3 cm l = 2 m \to cm = 2 \cdot 100 cm = 200 cm D_{2} = D_{1} + 2 \cdot h = 10 + 2 \cdot 0.3 = \frac{53}{5} = 10.6 cm r_{1} = D_{1} / 2 = 10 / 2 = 5 cm r_{2} = D_{2} / 2 = 10.6 / 2 = \frac{53}{10} = 5.3 cm S = π \cdot r_{2}^{2} - π \cdot r_{1}^{2} = 3.1416 \cdot 5. 3^{2} - 3.1416 \cdot 5^{2} ≐ 9.7075 {cm}^{2} V = S \cdot l = 9.7075 \cdot 200 ≐ 1941.5043 {cm}^{3} r = 7.8 {g/cm}^{3} m_{1} = r \cdot V = 7.8 \cdot 1941.5043 ≐ 15143.7332 g m = m_{1} \to kg = m_{1} / 1000 kg = 15143.7332 / 1000 kg = 15.144 kg = 15.1437 kg

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