A cylindrical tank with a radius of 3 meters and a height of 10 meters is filled with water. If the water is transferred to a rectangular tank with dimensions 4 meters by 5 meters, what will be the height of the water in the rectangular tank?
["Cylindrical Tank to Rectangular Tank: How High Will the Water Rise?", "When transferring water from a cylindrical tank to a rectangular tank, understanding volume conversion is essential. This scenario involves a cylindrical tank with a radius of 3 meters and a height of 10 meters, filled completely with water. The water is then transferred into a rectangular tank measuring 4 meters in length and 5 meters in width, but only 5 meters in height.", "### Step-by-Step: Calculating Water Height in the Rectangular Tank", "Step 1: Calculate the volume of water in the cylindrical tank", "The formula for the volume of a cylinder is:", "[\nV = \pi r^2 h\n]", "Given:\n- Radius ( r = 3 , \ ext{m} )\n- Height ( h = 10 , \ ext{m} )", "Substitute values:", "[\nV = \pi \ imes 3^2 \ imes 10 = \pi \ imes 9 \ imes 10 = 90\pi , \ ext{cubic meters}\n]", "Using ( \pi \approx 3.1416 ),", "[\nV \approx 90 \ imes 3.1416 = 282.74 , \ ext{m}^3\n]", "Step 2: Use volume to find water height in the rectangular tank", "The volume of water remains constant during transfer. The rectangular tank has:", "- Length ( l = 4 , \ ext{m} )\n- Width ( w = 5 , \ ext{m} )\n- Cross-sectional area ( A = l \ imes w = 4 \ imes 5 = 20 , \ ext{m}^2 )", "Let ( h_{\ ext{new}} ) be the height of water in the rectangular tank. Volume formula is:", "[\nV = A \ imes h_{\ ext{new}}\n]", "Rearranged:", "[\nh_{\ ext{new}} = \frac{V}{A} = \frac{90\pi}{20} = \frac{282.74}{20} \approx 14.14 , \ ext{meters}\n]", "However, the rectangular tank has only a maximum height of 5 meters. Since ( 14.14 , \ ext{m} > 5 , \ ext{m} ), the water cannot fill more than the tank’s height.", "Conclusion:\nThe water will fill the rectangular tank to its maximum capacity of 5 meters.", "### Ready to Use", "This example highlights how volume conservation across different tank shapes determines final water levels. While the cylindrical tank contains about 282.74 m³ of water, the rectangular tank — despite sharing a base area of 20 m² — cannot hold more than 5 meters of water. Therefore, the transferred volume fills the rectangular tank to exactly 5 meters.", "---", "Keywords: cylindrical tank volume, rectangular tank water height, water transfer calculation, water filled tank height, volume of cylinder to rectangular tank, how tall will water rise, cylindrical to rectangular tank conversion", "Meta Description:\nDiscover how a cylindrical tank with a 3m radius and 10m height fills a rectangular tank of 4m × 5m dimensions, calculating precise water height with volume conservation principles."]
