A cylindrical tank with a radius of 3 meters and height of 5 meters is filled with water. If the water is drained at a rate of 2 cubic meters per minute, how long will it take to empty the tank?
["How Long to Drain a Cylindrical Water Tank? A Practical Calculation", "Managing water storage efficiently is crucial in residential, agricultural, and industrial settings where cylindrical water tanks are commonly used. A typical cylindrical tank with a radius of 3 meters and a height of 5 meters can hold a significant volume of water. Understanding how long it takes to drain such a tank—especially when drained at a controlled rate—helps with planning maintenance, emergency response, and resource allocation.", "### Understanding the Volume of the Cylindrical Tank", "The volume ( V ) of a cylinder is calculated using the formula:\n[\nV = \pi r^2 h\n]\nwhere:\n- ( r ) is the radius,\n- ( h ) is the height,\n- ( \pi ) is approximately 3.1416.", "Given:\n- Radius ( r = 3 ) meters\n- Height ( h = 5 ) meters", "Substituting these values:\n[\nV = \pi \ imes (3)^2 \ imes 5 = \pi \ imes 9 \ imes 5 = 45\pi \ ext{ cubic meters}\n]\nUsing ( \pi \approx 3.1416 ):\n[\nV \approx 45 \ imes 3.1416 = 141.372 \ ext{ cubic meters (m³)}\n]", "### Draining Rate and Time to Empty the Tank", "The water is drained at a constant rate of 2 cubic meters per minute. To find the total time required to empty the tank, divide the total volume by the drainage rate:\n[\n\ ext{Time} = \frac{\ ext{Total Volume}}{\ ext{Drain Rate}} = \frac{141.372}{2} = 70.686 \ ext{ minutes}\n]", "### Rounded Result", "Rounding to a practical precision:\nApproximately 70.7 minutes (or about 1 hour and 1 minute) is the time needed to fully drain the tank.", "---", "### Summary", "- A cylindrical tank with a radius of 3 meters and height of 5 meters holds roughly 141.37 m³ of water.\n- Draining this volume at 2 m³ per minute takes about 70.7 minutes.\n- This calculation helps in estimating downtime, planning water supply alternates, and scheduling maintenance in systems relying on such tanks.", "Efficient water management begins with precise volume calculations—and knowing how long drainage takes ensures reliable planning. Whether for homes, farms, or commercial facilities, understanding tank drain times supports better operational control."]
