#### 7.331. A cylindrical tank with a radius of 5 meters and a height of 10 meters is filled with water. Calculate the volume of water in the tank, using π ≈ 3.14.

["Title: How to Calculate the Volume of a Cylindrical Water Tank – A Practical Example (7.331 m³ Demystified)", "---", "Introduction\nUnderstanding how to calculate the volume of a cylindrical tank is essential in fields like construction, agriculture, engineering, and water management. In this article, we’ll explore the formula for finding the volume of a cylinder using real-world data: a tank with a radius of 5 meters and a height of 10 meters, filled completely with water. We’ll walk step-by-step through the calculation using π ≈ 3.14 and derive a clear answer—arriving at a total volume of approximately 7,331 cubic meters.", "---", "### Why Calculate the Volume of Water?", "Accurately determining the water volume in a cylindrical tank helps with:", "- Managing water supply for industrial, agricultural, or household use\n- Sizing pumps and filtration systems\n- Planning storage solutions and avoiding overflow\n- Supporting engineering and environmental studies", "---", "### The Formula for the Volume of a Cylinder", "The volume ( V ) of a cylinder is calculated using:", "[\nV = \pi r^2 h\n]", "Where:\n- ( r ) = radius of the base\n- ( h ) = height (or length) of the cylinder\n- ( \pi ) ≈ 3.14 (standard approximation for simplicity)", "---", "### Applying the Values to the Example Tank", "Given:\n- Radius ( r = 5 ) meters\n- Height ( h = 10 ) meters\n- ( \pi \approx 3.14 )", "Step-by-step calculation:", "1. Square the radius:\n [\n r^2 = 5^2 = 25\n ]", "2. Multiply by the height:\n [\n r^2 \ imes h = 25 \ imes 10 = 250\n ]", "3. Multiply by π:\n [\n V = 3.14 \ imes 250 = 785\n ]", "Wait — at first glance, this gives us 785 m³, but let's double-check:\nHold on! This result seems much lower than the expected 7,331 m³. Let's re-evaluate carefully.", "---", "### Identifying the Reason for the Mismatch", "To achieve a volume of ~7,331 m³, we need to reconsider the units or values. This volume suggests the radius or height—or both—might have been incorrectly interpreted.", "Let’s solve for the correct volume by reversing the logic based on a known formula output:", "Suppose we seek when:\n[\nV = \pi r^2 h \quad \Rightarrow \quad r^2 h = \frac{V}{\pi}\n]", "With:\n- ( V = 7331 , \ ext{m}^3 )\n- ( \pi \approx 3.14 )\n- So:\n [\n r^2 h = \frac{7331}{3.14} \approx 2333.45\n ]", "Now test plausible values matching the given radius of 5 m:", "[\nr^2 = 5^2 = 25\n\Rightarrow h = \frac{2333.45}{25} \approx 93.34 , \ ext{m}\n]", "This exceeds the 10 m height — indicating the volume value 7,331 m³ likely refers to a misstatement unless the dimensions are different.", "---", "### Correct Interpretation & Final Answer", "Given:\n- Radius = 5 meters\n- Height = 10 meters\n- ( \pi \approx 3.14 )", "Correct volume calculation:\n[\nV = \pi r^2 h = 3.14 \ imes 25 \ imes 10 = 3.14 \ imes 250 = 785 , \ ext{m}^3\n]", "So, a cylindrical tank with a 5-meter radius and 10-meter height holds exactly 785 cubic meters of water.", "---", "### Why do people sometimes see “7,331 m³”?", "The number 7,331 may arise from combining multiple factors:", "- Volume of multiple tanks\n- Use of a different radius or height in a variant problem\n- Rounding π differently (e.g., π ≈ 3.1416) leading to higher precision\n- Misinterpretation linking cubic meters to other units (e.g., 7331 liters = 7.331 m³ — which is off by a factor of 1000)", "---", "### Conclusion", "While the desired volume of ~7,331 m³ does not match the cylinder dimensions of radius 5 m and height 10 m (which yield 785 m³), accurate volume calculations rely on correct data and formulas. Remember:", "[\n\boxed{\ ext{A cylindrical tank with radius } r = 5,\ ext{m and height } h = 10,\ ext{m holds } 785,\ ext{m}^3\ ext{ of water—calculated using } V = \pi r^2 h \approx 3.14 \ imes 25 \ imes 10 = 785\n]", "For real-world applications, always verify dimensions and use consistent units to avoid errors. Mastery of cylindrical volume calculations empowers better management of water systems and infrastructure design.", "---", "Keywords: water tank volume, cylindrical tank calculation, how to calculate cylinder volume, π approximation 3.14, water storage volume, geometry formula, tank capacity, volume in cubic meters, engineering calculations", "Meta Description: Learn how to calculate the volume of a cylindrical water tank with radius 5 m and height 10 m using π ≈ 3.14. Discover step-by-step formula, real-world applications, and why 7,331 m³ typically requires corrected dimensions."]