# 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 =  15.144 kg

#### Solution:

$D_{1}=10 \ \text{cm} \ \\ h=3 \ mm \rightarrow cm=3 / 10 \ cm=0.3 \ cm \ \\ l=2 \ m \rightarrow cm=2 \cdot \ 100 \ cm=200 \ cm \ \\ \ \\ D_{2}=D_{1}+2 \cdot \ h=10+2 \cdot \ 0.3=\dfrac{ 53 }{ 5 }=10.6 \ \text{cm} \ \\ \ \\ r_{1}=D_{1}/2=10/2=5 \ \text{cm} \ \\ r_{2}=D_{2}/2=10.6/2=\dfrac{ 53 }{ 10 }=5.3 \ \text{cm} \ \\ \ \\ S=\pi \cdot \ r_{2}^2 - \pi \cdot \ r_{1}^2=3.1416 \cdot \ 5.3^2 - 3.1416 \cdot \ 5^2 \doteq 9.7075 \ \text{cm}^2 \ \\ \ \\ \ \\ V=S \cdot \ l=9.7075 \cdot \ 200 \doteq 1941.5043 \ \text{cm}^3 \ \\ \ \\ r=7.8 \ \text{g/cm}^3 \ \\ m_{1}=r \cdot \ V=7.8 \cdot \ 1941.5043 \doteq 15143.7332 \ \text{g} \ \\ \ \\ m=m_{1} \rightarrow kg=m_{1} / 1000 \ kg=15143.733227364 / 1000 \ kg=15.144 \ kg=15.144 \ \text{kg}$

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