Embankment

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

Correct result:

V =  13200 m³

Solution:

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

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