Cross-section of iron bar

What is the mass of an iron bar 1.5 m long, the cross-section of which is a rhombus with side a = 45 mm and a corresponding height of 40 mm? Iron density ρ = 7.8 g/cm³? What is the surface of the iron rod?

Correct answer:

m =  21.06 kg
S =  0.2736 m²

Step-by-step explanation:

$$\begin{gathered} c=1.5\text{m} \\ a=45\text{mm}\to \text{m}=45:1000\text{m}=0.045\text{m} \\ v=40\text{mm}\to \text{m}=40:1000\text{m}=0.04\text{m} \\ \rho =7.8{\text{g/cm}}^3\to {\text{kg/m}}^3=7.8\cdot 1000{\text{kg/m}}^3=7800{\text{kg/m}}^3 \\ {S}_1=a\cdot v=0.045\cdot 0.04=\frac{9}{5000}=0.0018{\text{m}}^2 \\ V=S_1\cdot c=0.0018\cdot 1.5=\frac{27}{10000}=0.0027{\text{m}}^3 \\ m=\rho \cdot V=7800\cdot 0.0027=21.06\text{kg} \end{gathered}$$

$$\begin{gathered} S_2=4\cdot a\cdot c=4\cdot 0.045\cdot 1.5=\frac{27}{100}=0.27{\text{m}}^2 \\ S=S_2+2\cdot S_1=0.27+2\cdot 0.0018=0.2736{\text{m}}^2 \end{gathered}$$

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