A cylindrical tank has a radius of 3 meters and a height of 5 meters. If the tank is filled with water, what is the volume of the water in cubic meters?
["# Understanding the Volume of a Cylindrical Water Tank", "When managing water storage in residential, agricultural, or industrial settings, understanding tank capacity is essential. For example, consider a cylindrical water tank with a radius of 3 meters and a height of 5 meters. Knowing its volume in cubic meters not only helps optimize water management but also aids in planning plumbing, pumping systems, and maintenance schedules.", "In this article, we’ll calculate the volume of water that a cylindrical tank can hold when fully filled, using key geometric formulas. Whether you’re a homeowner planning a rainwater collection system or a facility manager ensuring adequate water supply, this guide explains how to determine the tank’s capacity efficiently.", "## The Geometry of a Cylindrical Tank", "A cylinder’s volume is derived from its two fundamental properties: radius and height. The formula to calculate the volume ( V ) of a cylinder is:", "[ V = \pi r^2 h ]", "Where:\n- ( r ) = radius of the circular base\n- ( h ) = height (or depth) of the cylinder\n- ( \pi ) (pi) ≈ 3.14159", "This formula calculates the space enclosed within the curved metallic or concrete walls of the tank when full. Since the tank is idealized as a perfect cylinder, all internal space available is available for water.", "## Step-by-Step Volume Calculation", "Let’s plug the given measurements into the formula. The tank has a radius $ r = 3 $ meters and a height $ h = 5 $ meters.", "1. Square the radius:\n [\n r^2 = 3^2 = 9 \ ext{ m}^2\n ]", "2. Multiply by the height:\n [\n 9 \ imes 5 = 45 \ ext{ m}^2\n ]", "3. Multiply by $ \pi $:\n [\n V = \pi \ imes 45 \approx 3.14159 \ imes 45 \approx 141.37 \ ext{ m}^3\n ]", "Thus, the total volume of water the tank holds when full is approximately 141.37 cubic meters.", "## Precision and Practical Applications", "For most practical purposes, rounding the volume to 141.4 m³ or using the exact expression ( 45\pi ) m³ provides sufficient accuracy. However, in engineering and design contexts, using ( \pi \approx 3.1416 ) or a high-precision calculator ensures reliable results for cost estimation and material specifications.", "This precise volume measurement enables efficient planning:\n- Estimating water availability for daily use\n- Sizing pumps and filtration systems\n- Budgeting for water capture and distribution\n- Monitoring storage levels in smart irrigation or industrial tanks", "## Conclusion", "A cylindrical tank with a 3-meter radius and 5-meter height holds approximately 141.37 cubic meters of water when full. Understanding this volume empowers better resource management and infrastructure planning. Whether installing a new tank or evaluating existing capacity, knowing the formula and calculation process ensures accurate, cost-effective water storage solutions.", "For optimal performance, always use precise values of ( \pi ) and confirm measurements to avoid costly errors in tank design and operation."]
