Question

An irrigation canal is 10 kilometers long and 2 meters deep. It is 4 meters wide at the 2 meters wide at the bottom. How many cubic meters of earth were excavated to make the canal?

Answer 1

The cross section of the canal will form a trapezoid. First, find the area of the cross section. The area of a trapezoid is defined as

`\begin{gathered} A_{\text{trapezoid}}=(a+b)/(2)h \\ \\ \text{Given} \\ h=2\text{ meters (2 meters deep)} \\ a=4\text{ meters (4 meters wide)} \\ b=2\text{ meters (2 meters wide at the bottom)} \end{gathered}`

Substitute the following values and we get the area

`\begin{gathered} A=(a+b)/(2)h \\ A=(4+2)/(2)(2) \\ A=(6)/(2)(2) \\ A=6\text{ m}^2 \end{gathered}`

Now that we have the area of the cross section, multiply it to the length of the irrigation canal.

Therefore, they have to excavate 60,000 cubic meters of earth to make the canal.