A cylindrical tank with a radius of 5 meters and a height of 10 meters is filled with water. Calculate the volume of water in the tank in cubic meters using the formula for the volume of a cylinder \( V = \pi r^2 h \).
["# Understanding the Volume of a Cylindrical Water Tank: A Detailed Calculation", "When managing water storage in industrial, agricultural, or municipal systems, cylindrical tanks are widely used due to their efficient space utilization and structural durability. One common configuration features a cylindrical tank with a radius of 5 meters and a height of 10 meters, filled completely with water. Understanding the volume of water it holds is essential for accurate resource planning and distribution.", "## What is the Volume of a Cylinder?", "The volume of a cylinder is calculated using the fundamental geometric formula:", "[\nV = \pi r^2 h\n]", "where:\n- ( V ) = volume in cubic meters (m³)\n- ( r ) = radius of the circular base in meters\n- ( h ) = height of the cylinder in meters\n- ( \pi ) (pi) ≈ 3.1416", "This formula derives from the area of the circular base (( \pi r^2 )) multiplied by the vertical height (( h )), extending the 2D area into a 3D volume.", "## Applying the Formula to the Given Tank", "For the cylindrical water tank:\n- Radius ( r = 5 ) meters\n- Height ( h = 10 ) meters", "Substitute these values into the volume formula:", "[\nV = \pi \ imes (5)^2 \ imes 10\n]", "First, calculate the square of the radius:", "[\nr^2 = 5^2 = 25 , \ ext{m}^2\n]", "Now multiply by the height and ( \pi ):", "[\nV = \pi \ imes 25 \ imes 10 = 250\pi , \ ext{m}^3\n]", "Using ( \pi \approx 3.1416 ):", "[\nV \approx 250 \ imes 3.1416 = 785.4 , \ ext{m}^3\n]", "## Conclusion", "The cylindrical tank with a radius of 5 meters and a height of 10 meters holds approximately 785.4 cubic meters of water when fully filled. This volume data is vital for capacity planning, ensuring the tank meets specific water supply demands in residential, agricultural, or industrial water systems.", "Understanding these calculations enables engineers, facility managers, and planners to optimize water storage solutions efficiently and sustainably. Whether for firefighting reserves, irrigation, or daily consumption, accurate volume measurement ensures reliable water availability."]
