Trench

The trench is a four-sided prism. The cross section has a trapezoidal shape with basements of 4m and 6m, the length of the trench is 30m. What is the depth of the trench if we dig 60,000 l of soil.

Correct result:

h =  0.4 m

Solution:

$$\begin{gathered} a=4\text{ m } \\ c=6\text{ m } \\ s=(a+c)\mathrm{/}2=(4+6)\mathrm{/}2=5\text{ m } \\ l=30\text{ m } \\ V=60000\mathrm{/}1000=60{\text{m}}^3 \\ S=V\mathrm{/}l=60\mathrm{/}30=2{\text{m}}^2 \\ S=s\cdot h \\ h=S\mathrm{/}s=2\mathrm{/}5={\displaystyle \frac{2}{5}}={\displaystyle \frac{2}{5}}\text{ m}=0.4\text{ m} \end{gathered}$$

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