A cylindrical tank with a radius of 3 meters and a height of 10 meters is filled with water. If water is drained until the height is reduced by 4 meters, what is the volume of water remaining in the tank?
["How To Calculate the Volume of Water Remaining in a Cylindrical Tank After Draining", "When managing water storage systems—such as industrial tanks, water towers, or reservoirs—understanding the remaining volume after partial draining is essential. This guide explains how to calculate the volume of water left in a cylindrical tank after lowering its water level, using a practical example involving a tank with a radius of 3 meters and a height of 10 meters.", "---", "### The Problem Setup", "Consider a cylindrical water tank with:\n- Radius ( r = 3 ) meters\n- Full height ( h = 10 ) meters\n- Initially full of water", "After draining, the water level decreases by 4 meters. We need to compute the volume of water remaining in the tank.", "---", "### Step 1: Understand the Cylinder Volume Formula", "The volume ( V ) of a full cylinder is given by:\n[\nV = \pi r^2 h\n]\nBut since the tank is partially filled, we calculate the volume of the remaining water using the updated height.", "---", "### Step 2: Determine the Remaining Water Height", "Initial height of water = 10 meters\nHeight drained = 4 meters\nRemaining height ( h_{\ ext{remaining}} = 10 - 4 = 6 ) meters", "---", "### Step 3: Calculate the Remaining Volume", "Using the cylinder volume formula with the remaining height:\n[\nV_{\ ext{remaining}} = \pi r^2 h_{\ ext{remaining}}\n]", "Substitute the values:\n[\nV_{\ ext{remaining}} = \pi (3)^2 \ imes 6 = \pi \ imes 9 \ imes 6 = 54\pi \ \ ext{cubic meters}\n]", "---", "### Step 4: Final Answer (Approximate Value for Readability)", "Using ( \pi \approx 3.1416 ),\n[\n54\pi \approx 54 \ imes 3.1416 = 169.65 \ \ ext{cubic meters}\n]", "So, the volume of water remaining in the tank is approximately 169.65 m³, or exactly ( 54\pi ) m³.", "---", "### Why This Calculation Matters", "- Effective water resource management\n- Proper tank design and capacity planning\n- Accurate cost estimation for water supply systems", "---", "### Summary", "A cylindrical tank with a 3-meter radius filled to 10 meters holds 54π cubic meters (≈169.65 m³) of water. After draining 4 meters of water, the remaining volume is calculated using the same radius but reduced height—simple yet vital for engineering and operational decisions.", "---", "Keywords: cylindrical tank volume, water drained from cylinder, remaining water volume, cylinder water capacity, water tank calculation, cylindrical tank height reduction, cylinder volume formula", "---", "For optimal water handling and system design, always compute remaining volume using the final liquid height and the cylindrical volume equation."]
