A cylindrical tank with radius 3 meters and height 10 meters is filled with water (density 1,000 kg/m³). What is the mass of the water in kilograms?
["Title: How to Calculate the Mass of Water in a Cylindrical Tank – A Practical Example", "When working with cylindrical tanks filled with liquids like water, understanding how to calculate the mass is essential—especially in industries such as engineering, construction, and resource management. In this article, we explore a specific case: a cylindrical tank with a radius of 3 meters and a height of 10 meters, completely filled with water (density = 1,000 kg/m³). We’ll walk through the complete calculation of the water’s mass and explain the key formulas involved.", "---", "### Understanding the Problem", "We are given:", "- Radius (r): 3 meters\n- Height (h): 10 meters\n- Density of water (ρ): 1,000 kg/m³", "The tank’s volume must first be determined to find how much water it holds. Since the tank is cylindrical, its volume ( V ) is calculated using the formula:", "[\nV = \pi r^2 h\n]", "---", "### Step-by-Step Calculation", "Step 1: Plug values into the volume formula", "[\nV = \pi (3)^2 (10) = \pi \ imes 9 \ imes 10 = 90\pi , \ ext{m}^3\n]", "Using ( \pi \approx 3.1416 ):", "[\nV \approx 90 \ imes 3.1416 = 282.74 , \ ext{m}^3\n]", "Step 2: Use density to find mass", "Mass ( m ) is mass density times volume:", "[\nm = \rho \ imes V = 1,000 , \ ext{kg/m}^3 \ imes 282.74 , \ ext{m}^3 = 282,740 , \ ext{kg}\n]", "---", "### Final Result", "The total mass of water in the cylindrical tank is approximately 282,740 kilograms.", "---", "### Why This Calculation Matters", "Accurate mass estimation is vital for:", "- Structural load planning: Supporting heavy tanks requires careful weight assessment.\n- Pumping and transfer operations: Knowing the water mass helps size pumps and pipelines.\n- Environmental and safety regulations: Compliance often depends on precise volume and weight data.", "---", "### Summary", "- A cylinder with radius 3 m and height 10 m holds volumetrically ( 90\pi , \ ext{m}^3 ), or about 282.74 m³.\n- At standard water density, this volume contains roughly 282,740 kg of water.\n- Mastering these calculations supports efficient design and management of water storage systems.", "---", "Keywords: cylindrical tank mass calculation, water density kg/m³, volume of cylinder formula, water mass kg, cylindrical tank water weight, fluid mechanics, liquid storage capacity, engineering calculations.", "---", "Optimize your tank management today—know your water load with precision!"]
