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 cuboidal tank with a base area of 45 square meters, what is the height of the water in the cuboidal tank?
["Title: How to Calculate Water Height in a Cuboidal Tank – Real-World Example with Precise Math", "When managing water storage in industrial or municipal systems, understanding volume conversion is essential. In this detailed article, we explore a practical scenario: transferring water from a cylindrical tank into a cuboidal tank and calculating the resulting water height.", "### Scenario Overview", "We begin with a cylindrical water tank characterized by a radius of 3 meters and a height of 10 meters, fully filled with water. This cylindrical tank is then emptied into a cuboidal (rectangular prism) tank with a base area of 45 square meters. Our goal is to determine the height of the transferred water in the cuboidal tank.", "---", "### Step 1: Calculate Volume of Water in the Cylindrical Tank", "The volume ( V ) of a cylinder is given by the formula:\n[\nV = \pi r^2 h\n]\nwhere ( r ) is the radius and ( h ) is the height.", "Given:\n- Radius ( r = 3 , \ ext{m} )\n- Height ( h = 10 , \ ext{m} )", "Substitute values:\n[\nV = \pi (3)^2 (10) = \pi \ imes 9 \ imes 10 = 90\pi , \ ext{m}^3\n]", "Using the approximation ( \pi \approx 3.1416 ),\n[\nV \approx 90 \ imes 3.1416 = 282.74 , \ ext{m}^3\n]\n(Alternatively, exact: ( 90\pi , \ ext{m}^3 ))", "---", "### Step 2: Relate Volume to Cuboidal Tank’s Height", "The cuboidal tank has:\n- Base area = 45 m²\n- Volume = area × height\nLet ( H ) be the height of water in the cuboidal tank.", "So,\n[\n\ ext{Volume} = \ ext{Base Area} \ imes \ ext{Height} = 45 \ imes H\n]", "Set this equal to the water volume from the cylinder:\n[\n45H = 90\pi\n]", "Solve for ( H ):\n[\nH = \frac{90\pi}{45} = 2\pi\n]", "Using ( \pi \approx 3.1416 ),\n[\nH \approx 2 \ imes 3.1416 = 6.2832 , \ ext{meters}\n]", "---", "### Final Result", "The water transferred from the cylindrical tank fills the cuboidal tank to a height of approximately 6.28 meters.", "### Why This Calculation Matters", "- Efficient water management: Accurate volume transfer ensures no overfill or underestimation.\n- Planning for infrastructure: Engineers and facility managers rely on such precise conversions for tank selection and capacity planning.\n- Real-world applications: Municipal water systems, agricultural irrigation, stormwater management—all benefit from clear hydrological calculations.", "---", "### Key Takeaways", "- Cylindrical tank volume = ( 90\pi , \ ext{m}^3 )\n- Cuboidal tank height = ( \frac{90\pi}{45} = 2\pi , \ ext{m} )\n- Final water height ≈ 6.28 meters", "Understanding these principles enables smarter and safer water storage solutions across many domains.", "---", "Keywords: cylindrical tank volume, cuboid tank height calculation, water transfer height, water storage tank conversion, volume to height formula, 3 meter radius tank, 10 meter tall cylinder, cuboidal tank with 45 m² base, muetage d’eau, engineering calculation", "---", "Stay informed. Calculate wisely. Store water efficiently."]
