A cylindrical water tank has a radius of 3 meters and a height of 5 meters. If the tank is filled to 80% of its capacity, how many cubic meters of water does it contain?
["Title: How Much Water Does a Cylindrical Tank Hold? Calculating Capacity and Filled Volume", "When designing or assessing water storage systems, understanding a cylindrical tank’s capacity plays a crucial role—especially for applications in agriculture, residential supply, or industrial use. In this article, we’ll explore the volume of a cylindrical water tank with a radius of 3 meters and a height of 5 meters, specifically calculating how much water it holds when filled to 80% of its total capacity.", "### Understanding the Geometry of a Cylinder", "A cylinder’s volume is determined using the well-known formula:", "[\nV = \pi r^2 h\n]", "where:\n- ( V ) = volume in cubic meters\n- ( r ) = radius of the base\n- ( h ) = height of the cylinder", "For this tank, the radius ( r = 3 ) meters and the height ( h = 5 ) meters.", "### Calculating Full Tank Capacity", "Substituting 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 ), we estimate:", "[\n45 \ imes 3.1416 \approx 141.37 \ ext{ cubic meters}\n]", "So, the full capacity of the tank is approximately 141.37 cubic meters.", "### Determining Fill Level: 80% Capacity", "To find out how much water the tank contains when filled to 80%, multiply the full volume by 0.80:", "[\n0.80 \ imes 45\pi = 36\pi \ ext{ cubic meters}\n]", "Numerically, this equals:", "[\n36 \ imes 3.1416 \approx 113.10 \ ext{ cubic meters}\n]", "### Practical Implications and Design Insights", "Understanding that a 3-meter-radius, 5-meter-tall cylindrical tank holds about 113.10 cubic meters of water at 80% capacity helps in planning water supply schedules, pump sizing, and overflow management. Whether used in rural homes, farms, or municipal systems, accurately calculating storage capacity ensures efficient resource management and prevents under- or overestimation of water availability.", "### Summary", "- Cylinder radius: 3 meters\n- Height: 5 meters\n- Full volume: ( 45\pi \approx 141.37 , \ ext{m}^3 )\n- 80% filled volume: ( 36\pi \approx 113.10 , \ ext{m}^3 )", "This data provides a solid foundation for anyone assessing or designing cylindrical water tanks—supporting informed decisions and reliable performance in real-world applications.", "---", "Keywords: cylindrical water tank capacity, water tank volume calculation, cylindrical tank 3 meter radius, water storage 80% capacity, cylinder volume formula, water storage system, cylindrical tank calculation."]
