Road embankment

Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters?

Correct result:

x =  15318.26 m3

Solution:

 v2=b2ac2 v=b2ac2=b2ac2=1.73 m S=a+c2v=10.39 m2 V=Sl=10.391474=15318.26 m3 \ \\ v^2 = b^2-\dfrac{a-c}{2} \ \\ v = \sqrt{b^2-\dfrac{a-c}{2}}= \sqrt{b^2-\dfrac{a-c}{2}} = 1.73 \ m \ \\ S = \dfrac{ a+ c}{2}v = 10.39 \ m^2 \ \\ V = S \cdot l = 10.39 \cdot 1474 = 15318.26 \ \text{m}^3



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