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:

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

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