A cylindrical tank with a radius of 3 meters and a height of 5 meters is filled with water. If 20% of the water is drained, what is the volume of the remaining water in the tank (in cubic meters)?
["Understanding the Volume of Water Remaining in a Cylindrical Tank", "When managing water storage in industrial, agricultural, or municipal systems, accurate calculation of liquid volume is essential. One common scenario involves cylindrical tanks—widely used for their efficiency and durability. Consider a cylindrical tank with a radius of 3 meters and a height of 5 meters. If this tank is filled with water and 20% of the water is drained, how much water remains? This article explores the cylindrical tank volume calculation, the impact of partial drainage, and the final remaining volume in cubic meters.", "---", "### The Geometry of a Cylindrical Tank", "A cylinder’s volume is determined by the formula:", "[\nV = \pi r^2 h\n]", "where:\n- ( r ) = radius of the base\n- ( h ) = height of the cylinder\n- ( \pi ) ≈ 3.1416", "In our case:\n- Radius ( r = 3 ) meters\n- Height ( h = 5 ) meters", "Plugging in the values:", "[\nV = \pi \ imes (3)^2 \ imes 5 = \pi \ imes 9 \ imes 5 = 45\pi \ ext{ cubic meters}\n]", "Using ( \pi \approx 3.1416 ), the full volume is:", "[\n45 \ imes 3.1416 \approx 141.372 \ ext{ cubic meters}\n]", "---", "### Calculating the Drained Volume", "If 20% of the water is drained, the volume drained is:", "[\n\ ext{Drained volume} = 0.20 \ imes 45\pi = 9\pi \ ext{ cubic meters}\n]", "Thus, the volume of water remaining in the tank is:", "[\n\ ext{Remaining volume} = 45\pi - 9\pi = 36\pi \ ext{ cubic meters}\n]", "Substituting ( \pi \approx 3.1416 ):", "[\n36 \ imes 3.1416 \approx 113.0976 \ ext{ cubic meters}\n]", "---", "### Final Answer", "The volume of water remaining in the cylindrical tank after draining 20% is approximately 113.1 cubic meters. This calculation ensures precise water management, supporting optimal use in irrigation, supply systems, or industrial processing.", "---", "### Key Takeaways", "- Cylindrical tanks offer consistent cross-sectional area, ideal for storage efficiency.\n- Volume depends directly on radius squared and height—small changes in dimensions affect capacity significantly.\n- Percentage-based draining is common in tank monitoring; knowing remaining volume supports informed operations.\n- Using ( \pi ) in calculations delivers accurate results, crucial for engineering and logistics planning.", "For businesses and planners relying on water storage, mastering these volumes improves operational control and resource forecasting."]
