A cylindrical tank with a radius of 5 meters is filled with water to a height of 10 meters. If the water is drained until the height is reduced by 2 meters, what is the volume of water removed?
["Title: How Much Water Is Drained from a Cylindrical Tank When Level Is Lowered?", "When managing water storage in cylindrical tanks, precise calculations are essential for efficient planning, especially in industrial, agricultural, or municipal applications. One common scenario involves determining the volume of water removed after reducing the water level in a cylindrical tank.", "### Understanding the Geometry of a Cylindrical Tank", "A cylindrical tank with a radius of 5 meters holds water initially up to a height of 10 meters. The water volume is calculated using the formula for the volume of a cylinder:", "[\nV = \pi r^2 h\n]", "Where:\n- ( r ) = radius (5 meters)\n- ( h ) = height of the water column", "Plugging in the values:", "[\nV_{\ ext{initial}} = \pi \ imes (5)^2 \ imes 10 = \pi \ imes 25 \ imes 10 = 250\pi \ ext{ cubic meters}\n]", "### Calculating the Volume Removed After Draining", "The tank’s water level is reduced by 2 meters, so the removed water corresponds to a smaller cylinder with the same radius (5 meters) but a height of 2 meters:", "[\nV_{\ ext{removed}} = \pi \ imes (5)^2 \ imes 2 = \pi \ imes 25 \ imes 2 = 50\pi \ ext{ cubic meters}\n]", "### Numerical Value and Practical Insight", "Approximating ( \pi \approx 3.1416 ), the volume removed is:", "[\nV_{\ ext{removed}} \approx 50 \ imes 3.1416 = 157.08 \ ext{ cubic meters}\n]", "This calculation allows facility managers and engineers to precisely track water usage, plan refills, and optimize storage efficiency—critical for maintaining reliable water supply systems.", "### Conclusion", "By draining water from a cylindrical tank with a 5-meter radius from 10 meters to 8 meters in height, exactly 50π cubic meters—or approximately 157.08 cubic meters—of water is removed. Accurate volume computations enhance operational transparency and resource management in water storage applications.", "Keywords: cylindrical tank, volume of water removed, cylinder volume formula, water storage, water drainage calculation, radius 5 meters, 10 meter height, 2 meter reduction, 50π cubic meters, π water volume, drying a cylindrical tank, water volume calculation."]
