Dimensions 83226

Calculate the weight of an iron bar 1.2 m long, whose cross-section is a trapezoid with dimensions a=10 cm c=8 cm and the distance between the bases v=6 cm. As we know, 1 cubic meter of iron weighs 7800 kg.

Correct answer:

m =  50.544 kg

Step-by-step explanation:

$$\begin{gathered} L=1.2\text{m} \\ a=10\text{cm}\to \text{m}=10:100\text{m}=0.1\text{m} \\ c=8\text{cm}\to \text{m}=8:100\text{m}=0.08\text{m} \\ v=6\text{cm}\to \text{m}=6:100\text{m}=0.06\text{m} \\ \rho =7800{\text{kg/m}}^3 \\ S=\frac{a+c}{2}\cdot v=\frac{0.1+0.08}{2}\cdot 0.06=\frac{27}{5000}=0.0054{\text{m}}^2 \\ V=S\cdot L=0.0054\cdot 1.2=\frac{81}{12500}\doteq 0.0065{\text{m}}^3 \\ m=\rho \cdot V=7800\cdot 0.0065=50.544\text{kg} \end{gathered}$$

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