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 answer:

m =  15.1437 kg

Step-by-step explanation:

$$\begin{gathered} D_1=10\text{cm} \\ h=3\text{mm}\to \text{cm}=3:10\text{cm}=0.3\text{cm} \\ l=2\text{m}\to \text{cm}=2\cdot 100\text{cm}=200\text{cm} \\ {D}_2=D_1+2\cdot h=10+2\cdot 0.3=\frac{53}{5}=10.6\text{cm} \\ {r}_1=D_1/2=10/2=5\text{cm} \\ {r}_2=D_2/2=10.6/2=\frac{53}{10}=5.3\text{cm} \\ S=\pi \cdot r_2^2-\pi \cdot r_1^2=3.1416\cdot 5.3^2-3.1416\cdot 5^2\doteq 9.7075{\text{cm}}^2 \\ V=S\cdot l=9.7075\cdot 200\doteq 1941.5043{\text{cm}}^3 \\ r=7.8{\text{g/cm}}^3 \\ {m}_1=r\cdot V=7.8\cdot 1941.5043\doteq 15143.7332\text{g} \\ m=m_1\to \text{kg}=m_1:1000\text{kg}=15143.7332:1000\text{kg}=15.144\text{kg}=15.1437\text{kg} \end{gathered}$$

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