The trench

Calculate how many cubic meters of soil needs to be removed from the excavation in the shape of an isosceles trapezoid, the top width is 3 meters, the lower width is 1.8 m, the depth of the excavation is 1 m, and the length is 20 m.

Correct result:

V =  48 m3

Solution:

l=20 m a=3 m c=1.8 m h=1 m  S=a+c2 h=3+1.82 1=125=2.4 m2  V=S l=2.4 20=48 m3l=20 \ \text{m} \ \\ a=3 \ \text{m} \ \\ c=1.8 \ \text{m} \ \\ h=1 \ \text{m} \ \\ \ \\ S=\dfrac{ a+c }{ 2 } \cdot \ h=\dfrac{ 3+1.8 }{ 2 } \cdot \ 1=\dfrac{ 12 }{ 5 }=2.4 \ \text{m}^2 \ \\ \ \\ V=S \cdot \ l=2.4 \cdot \ 20=48 \ \text{m}^3



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