Cross-section 8171

How many m³ of soil is to be excavated when digging a 120 m long ditch, the cross-section of which is an isosceles trapezoid with bases of 2.3 m and 3.3 m, if the depth of the trench is 90 cm?

Correct answer:

V =  309.42 m³

Step-by-step explanation:

$$\begin{gathered} l=120\text{m} \\ a=2.43\text{m} \\ c=3.3\text{m} \\ h=90\text{cm}\to \text{m}=90:100\text{m}=0.9\text{m} \\ {S}_1=\frac{a+c}{2}\cdot h=\frac{2.43+3.3}{2}\cdot 0.9=2.5785{\text{m}}^2 \\ V=S_1\cdot l=2.5785\cdot 120=\frac{15471}{50}{\text{m}}^3=309.42{\text{m}}^3 \end{gathered}$$

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