9. A railway tunnel $147 \mathrm{~m}$ long is to be bored with a circular cross section of radius $5 \mathrm{~m}$. What volume of soil has to be excavated? If the soil is to be taken away in wagons of capacity $75 \mathrm{~m}^{3}$ each, how many wagons are needed?
Answer
\(\boxed{\text{The volume of soil to be excavated is approximately 11545.35 cubic meters, and 154 wagons are needed to take away the soil.}}\)
Step 1 ：Given a railway tunnel with length \(l = 147\) meters and radius \(r = 5\) meters, we need to find the volume of soil to be excavated.
Step 2 ：Calculate the volume of the tunnel using the formula for the volume of a cylinder: \(V = \pi r^2 l\)
Step 3 ：\(V = \pi (5)^2 (147)\)
Step 4 ：\(V \approx 11545.35\) cubic meters
Step 5 ：The soil is to be taken away in wagons of capacity \(75\) cubic meters each. To find the number of wagons needed, divide the volume of soil by the capacity of each wagon.
Step 6 ：\(\text{Number of wagons} = \frac{11545.35}{75}\)
Step 7 ：\(\text{Number of wagons} \approx 154\)
Step 8 ：\(\boxed{\text{The volume of soil to be excavated is approximately 11545.35 cubic meters, and 154 wagons are needed to take away the soil.}}\)
