Trench

The trench is a four-sided prism. The cross-section has a trapezoidal shape with basements of 4m and 6m, and the length of the trench is 30m. What is the depth of the trench if we dig 60,000 l of soil?

Final Answer:

h =  0.4 m

Step-by-step explanation:

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

Try another example