A cylindrical tank with a radius of 3 meters and a height of 10 meters is filled with water. What is the volume of water in the tank? Use the formula \( V = \pi r^2 h \).
["Calculating the Volume of Water in a Cylindrical Tank", "When working with cylindrical structures, understanding their capacity—especially when filled with liquid like water—is essential in architecture, engineering, and water management. Today, we explore a concrete example: a cylindrical tank with a radius of 3 meters and a height of 10 meters, completely filled with water. Let’s calculate the volume of water using the fundamental formula for the volume of a cylinder.", "### The Formula: ( V = \pi r^2 h )", "The volume ( V ) of a cylinder is determined by multiplying the area of the circular base (( \pi r^2 )) by the height ( h ). This formula is widely used in engineering and construction to determine storage capacities and structural requirements.", "### Given Dimensions", "- Radius ( r = 3 ) meters\n- Height ( h = 10 ) meters\n- Use ( \pi \approx 3.1416 ) (standard decimal approximation)", "### Step-by-Step Calculation", "1. Calculate the area of the base:\n[\nr^2 = 3^2 = 9 , \ ext{m}^2\n]\n[\n\pi r^2 = \pi \ imes 9 \approx 3.1416 \ imes 9 = 28.2744 , \ ext{m}^2\n]", "2. Multiply by the height to get the volume:\n[\nV = \pi r^2 h = 28.2744 \ imes 10 = 282.744 , \ ext{m}^3\n]", "### Result and Interpretation", "The volume of water contained in the cylindrical tank is approximately 282.74 cubic meters. This means the tank can hold over 282,744 liters of water—enough to serve thousands of daily needs in residential or industrial applications.", "### Why This Matters", "Knowing the exact volume helps in planning water supply systems, assessing structural load, and optimizing storage space. For engineers and designers, this calculation is a baseline for projects involving cylindrical water storage tanks.", "---", "In summary, using the formula ( V = \pi r^2 h ), we confirmed that a cylindrical tank with a radius of 3 meters and a height of 10 meters holds precisely ( \approx 282.74 , \ ext{m}^3 ) of water—demonstrating how simple geometry enables precise hydrological calculations.", "Keywords: cylindrical tank volume, water volume formula, cylinder volume calculation, radius 3m height 10m, π formula application, water storage capacity."]
