Cross-section 33541

How many m³ of soil must be moved when digging a straight trench 170 m long, the cross-section of which is an isosceles trapezoid with bases of 150 cm and 80 cm, and arms are 90 cm long?

Correct answer:

x =  162.1 m³

Step-by-step explanation:

$$\begin{gathered} l=170\text{m} \\ a=150\text{cm}\to \text{m}=150:100\text{m}=1.5\text{m} \\ c=80\text{cm}\to \text{m}=80:100\text{m}=0.8\text{m} \\ r=90\text{cm}\to \text{m}=90:100\text{m}=0.9\text{m} \\ x=(a-c)/2=(\frac{3}{2}-\frac{4}{5})/2\doteq 162.1\text{m} \\ h=\sqrt{r^2-x^2}=\sqrt{0.9^2-162.1^2}\doteq 0.8292\text{m} \\ {S}_1=\frac{a+c}{2}\cdot h=\frac{1.5+0.8}{2}\cdot 0.8292\doteq 0.9535{\text{m}}^2 \\ x=S_1\cdot l=0.9535\cdot 170=162.1{\text{m}}^3 \end{gathered}$$

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