Embankment

The railway embankment is 300 m long and has a cross-section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate the amount of soil in the embankment in m³.

Correct answer:

V =  13200 m³

Step-by-step explanation:

$$\begin{gathered} l=300\text{m} \\ a=14\text{m} \\ c=8\text{m} \\ r=5\text{m} \\ x=\frac{a-c}{2}=\frac{14-8}{2}=3\text{m} \\ {r}^2=h^2+x^2 \\ h=\sqrt{r^2-x^2}=\sqrt{5^2-3^2}=4\text{m} \\ S=\frac{a+c}{2}\cdot h=\frac{14+8}{2}\cdot 4=44{\text{m}}^2 \\ V=l\cdot S=300\cdot 44=13200{\text{m}}^3 \end{gathered}$$

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