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.

Result

h =  0.4 m

Solution:

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

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