#### \( x = \frac{34}{13}, y = \frac{53}{13} \)1. **A cylindrical tank with a radius of 3 meters is filled with water to a height of 5 meters. Calculate the volume of water in the tank in cubic meters.

["Calculating the Volume of Water in a Cylindrical Tank: Step-by-Step Explanation", "When managing water storage in cylindrical tanks, understanding how to calculate volume is essential for efficient planning, resource management, and engineering. This guide walks through the calculation of the water volume in a cylindrical tank with specific dimensions: a radius of 3 meters and a water height of 5 meters.", "### Understanding the Cylinder Formula", "The volume ( V ) of a cylinder is calculated using the formula:\n[\nV = \pi r^2 h\n]\nwhere:\n- ( r ) = radius of the cylinder's base\n- ( h ) = height (or depth) of the liquid or contents\n- ( \pi ) (~3.1416) is a mathematical constant", "### Given Values in the Problem", "- Radius ( r = 3 ) meters\n- Water height ( h = 5 ) meters\n- The cylinder’s total height is not limiting since water fills only 5 meters, and the tank is taller (though not needed here).", "### Step-by-Step Calculation", "1. Square the radius:\n[\nr^2 = 3^2 = 9\n]", "2. Multiply by π:\n[\n\pi r^2 = \pi \ imes 9 \approx 3.1416 \ imes 9 = 28.2744\n]", "3. Multiply by the water height:\n[\nV = \pi r^2 h \approx 28.2744 \ imes 5 = 141.372 , \ ext{cubic meters}\n]", "### Final Volume", "The volume of water in the cylindrical tank is approximately:\n[\n\boxed{141.37 , \ ext{m}^3}\n]\n(rounded to two decimal places for practical measurement).", "### Key Takeaways", "- Accurate volume computation ensures proper water resource planning.\n- Cylinder shape simplifies volume calculation due to its regular geometric form.\n- The formula ( \pi r^2 h ) remains fundamental in real-world applications such as plumbing, agriculture, and industrial storage.", "For precision in engineering or daily use, always round or calculate using ( \pi \approx 3.1416 ) or more accurate constants when available."]