A cylindrical tank with a radius of 3 meters and a height of 5 meters is filled with water. If the water is drained at a rate of 0.5 cubic meters per minute, how long will it take to empty the tank completely?

Thu, 30 Apr 2026 18:19:17 +0000

A cylindrical tank with a radius of 3 meters and a height of 5 meters holds a substantial volume of water, offering a clear case study in fluid dynamics and practical water management. This tank stores approximately 70.65 cubic meters of water—calculated using the formula πr²h, where r = 3m and h = 5m. When drained at a steady rate of 0.5 cubic meters per minute, the expected emptying time totals 141.3 minutes, or roughly 2 hours and 21 minutes. This calculation aligns with growing real-world interest in irrigation, industrial water cycles, and sustainable resource monitoring. As communities and businesses increasingly focus on efficient water use, understanding such drainage timelines supports smarter planning and cost management. Why this topic is gaining visibility among U.S. audiences today? Water infrastructure and management remain critical conversations in regions facing drought stress, aging systems, or rising demand. Educational platforms and utility resources are highlighting these variables to empower homeowners, facility managers, and agricultural operators with actionable insights. By breaking down the math behind safe, realistic expectations, users gain clarity on timelines without guesswork—supporting informed decision-making across diverse applications. To precisely determine how long the water will drain, begin with the tank’s volume: using π ≈ 3.14, the cross-sectional area is π × 3² = 28.26 m². Multiply by height (5m): 28.26 × 5 ≈ 141.3 m³. Subtracting no losses for simplicity, 0.5 m³ per minute yields: 141.3 ÷ 0.5 = 282.6 minutes—wait, correction: 141.3 ÷ 0.5 equals 282.6? No—rechecking: 141.3 ÷ 0.5 = 282.6 minutes per first calculation, but wait—this contradicts prior. Let’s verify: Real recalc: πr² = π × 9 = 28.274 m². Volume = 28.274 × 5 = 141.37 m³. At 0.5 m³/min: 141.37 ÷ 0.5 = 282.74 minutes—so the original estimate of 141 minutes was incorrect. Correct total time is just over 2 hours and 21 minutes. This precision reflects growing demand for accurate, data-driven content users rely on for reliable planning and expectations.