Road embankment volume

The road embankment has a cross-section of an isosceles trapezoid with bases 16 m and 10 m long and with arms 5 m long. How many cubic meters of soil is in the 400 meters long dam?

Final Answer:

V =  20800 m³

Step-by-step explanation:

$$\begin{gathered} a=16\text{m} \\ c=10\text{m} \\ r=5\text{m} \\ l=400\text{m} \\ h=\sqrt{r^2-((a-c)/2{)}^2}=\sqrt{5^2-((16-10)/2{)}^2}=4\text{m} \\ S=\frac{a+c}{2}\cdot h=\frac{16+10}{2}\cdot 4=52{\text{m}}^2 \\ V=S\cdot l=52\cdot 400=20800{\text{m}}^3 \end{gathered}$$

Try another example