Hard Work in a Salt Mine
Underneath the town of Turda, Romania lies a huge complex of salt mines with a long history. Salt had been extracted from the region from over a thousand years ago, possibly earlier than the Middle Ages, and the mines continued operations until they closed in 1932. The mine was then used as a bunker during the air strikes of World War II. After the war, part of the mine was used as a cheese store. Then in 1992 it was opened to tourists.
The space is so large that one could fit a small amusement park down there. And that's exactly what they did! It has a Ferris wheel, a bowling alley, row boats, and mini golf. It was listed as one of "25 Unbelievable Travel Destinations You Never Knew Existed," which was exactly how I learned about it.
While I thoroughly enjoyed the amusement park, it was also very impressive to get to see the inside of a mine, especially one with such large spaces. It got me thinking about how much work it would have taken to mine so much salt, and that's a perfect problem for a calculus student to solve!
Sample Problems
1. The Terezia Mine is in the shape of a circular cone with height 90 meters and diameter 87 meters. Calculate the volume of this mine.
2. The Rudolf Mine is in the shape of a trapezoidal prism, with dimensions shown on the right. Calculate the volume of this mine.
3. Set up and evaluate an integral representing the amount of work it would take to lift the salt out of the Terezia mine to the entrance of the mine system, which was located 22 meters above the top of the cone-shaped mine. Use the fact that the density of rock salt is approximately 2165 kilograms per cubic meter.
4. Set up and evaluate an integral representing the amount of work it would take to lift the salt out of the Rudolf Mine to the entrance of the mine system, which was located at the ceiling of the Rudolf Mine. Again, use the fact that the density of rock salt is approximately 2165 kilograms per cubic meter.
Of course, this is just the work it would take to remove the salt. It does not include all of the actual excavation work in cutting the salt! No wonder it took so long to excavate the salt.
