A cylindrical tank with a radius of 3 meters and a height of 10 meters is filled with water. Calculate the volume of water in the tank in cubic meters, and then determine how many liters of water are in the tank. (Note: 1 cubic meter = 1000 liters)
["Understanding the Capacity of a Cylindrical Water Tank: Volume and Liters Explained", "When managing water storage systems—such as large industrial tanks or reservoirs—understanding the tank’s volume is essential for planning and usage. A common example is a cylindrical tank with a radius of 3 meters and a height of 10 meters filled completely with water. This article explains how to calculate the tank’s volume in cubic meters, converts that into liters, and provides practical insight into water capacity.", "---", "### How to Calculate the Volume of a Cylinder", "The volume ( V ) of a cylinder is given by the formula:", "[\nV = \pi r^2 h\n]", "where:\n- ( r ) is the radius of the base (in meters),\n- ( h ) is the height (in meters),\n- ( \pi ) (pi) is approximately 3.14159.", "For our tank:\n- Radius ( r = 3 ) meters\n- Height ( h = 10 ) meters", "Substituting the values:", "[\nV = \pi \ imes (3)^2 \ imes 10 = \pi \ imes 9 \ imes 10 = 90\pi\n]", "Using ( \pi \approx 3.14159 ):", "[\nV \approx 90 \ imes 3.14159 = 282.743 \ ext{ cubic meters (m³)}\n]", "So, the tank holds approximately 282.74 cubic meters of water when full.", "---", "### Converting Cubic Meters to Liters", "Since 1 cubic meter equals 1,000 liters, we convert the volume:", "[\n282.743 \ ext{ m}^3 \ imes 1,000 = 282,743 \ ext{ liters}\n]", "Thus, the tank contains 282,743 liters of water.", "---", "### Why This Matters", "This volume is significant for agriculture, firefighting, municipal supply, or stormwater management. Knowing exactly how many liters are stored allows for precise monitoring, efficient distribution planning, and capacity forecasting during supply shortages.", "---", "### Summary", "- Radius: 3 meters\n- Height: 10 meters\n- Volume: ( 90\pi \approx 282.74 , \ ext{m}^3 )\n- Liters: ( 282.74 \ imes 1000 = 282,743 , \ ext{liters} )", "For any cylindrical water tank, calculating volume using ( V = \pi r^2 h ) provides a reliable estimate of storage capacity—tying directly into practical water management needs. Whether designing new storage or assessing existing systems, this mathematical foundation ensures accuracy and efficiency."]
