# Embankment

The railway embankment 300 m long has a cross section of an isosceles trapezoid with bases of 14 m and 8 m. The trapezoidal arms are 5 m long. Calculate how much m3 of soil is in the embankment?

Correct result:

V =  13200 m3

#### Solution:

$l=300 \ \text{m} \ \\ a=14 \ \text{m} \ \\ c=8 \ \text{m} \ \\ r=5 \ \text{m} \ \\ \ \\ x=\dfrac{ a-c }{ 2 }=\dfrac{ 14-8 }{ 2 }=3 \ \text{m} \ \\ r^2=h^2+x^2 \ \\ h=\sqrt{ r^2-x^2 }=\sqrt{ 5^2-3^2 }=4 \ \text{m} \ \\ S=\dfrac{ a+c }{ 2 } \cdot \ h=\dfrac{ 14+8 }{ 2 } \cdot \ 4=44 \ \text{m}^2 \ \\ V=l \cdot \ S=300 \cdot \ 44=13200 \ \text{m}^3$

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