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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?

User Alexisvt
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1 Answer

24 votes
24 votes

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.


\begin{gathered} \text{Before multiplying, all units must be the same, convert km to meters} \\ 10\operatorname{km}\rightarrow10,000\text{ meters} \\ 6\text{ m}^2*10000\text{ meters} \\ \Longrightarrow60000\text{ m}^3 \end{gathered}

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

User Kerris
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