A cylindrical tank with a radius of 5 meters is filled with water to a height of 10 meters. If the radius is increased by 20%, what is the new volume?
["Optimizing Water Storage: How Increasing the Radius of a Cylindrical Tank Impacts Volume", "When designing water storage tanks, engineering precision is essential to maximize capacity and efficiency. This article explores a cylindrical water tank initially sized with a radius of 5 meters and a water height of 10 meters. We’ll examine how increasing the radius by 20% affects the tank’s total volume, offering key insights for engineers, architects, and facility managers aiming to optimize storage solutions.", "Understanding the Original Tank Volume", "The volume ( V ) of a cylinder is calculated using the formula:", "[\nV = \pi r^2 h\n]", "For the original tank:\n- Radius (( r )) = 5 meters\n- Height (( h )) = 10 meters", "Substituting values:", "[\nV = \pi (5)^2 (10) = \pi \cdot 25 \cdot 10 = 250\pi \ ext{ cubic meters}\n]", "This means the tank initially holds ( 250\pi , \ ext{m}^3 ) of water.", "Expanding the Radius: A 20% Increase", "Increasing the radius by 20% yields a new radius:", "[\nr_{\ ext{new}} = 5 + (20% \ imes 5) = 5 + 1 = 6 \ ext{ meters}\n]", "The height remains unchanged at 10 meters, so the new volume is:", "[\nV_{\ ext{new}} = \pi (6)^2 (10) = \pi \cdot 36 \cdot 10 = 360\pi \ ext{ cubic meters}\n]", "Comparing Volumes: A 44% Increase", "The volume increase from the original to the new tank is:", "[\n\Delta V = 360\pi - 250\pi = 110\pi , \ ext{m}^3\n]", "Expressed as a percentage increase:", "[\n\ ext{Volume Increase} = \left( \frac{110\pi}{250\pi} \right) \ imes 100% = 44%\n]", "Thus, increasing the radius by 20% results in a 44% increase in total volume—dramatically expanding storage capacity without altering height.", "Practical Considerations and Applications", "Raising the radius improves water storage while maintaining structural and material constraints. This adjustment is particularly valuable in settings requiring expanded reserves—such as rural water supply systems, industrial facilities, or emergency reserves. Engineers must consider factors like base stability, material costs, and ease of pumping, but enhancing radius offers one of the most direct paths to increasing volume.", "Conclusion", "A cylindrical tank with a 5-meter radius filled to 10 meters holds ( 250\pi , \ ext{m}^3 ) of water. When the radius is increased by 20% to 6 meters, the volume jumps to ( 360\pi , \ ext{m}^3 )—a 44% boost in capacity. This straightforward geometric adjustment demonstrates how subtle design changes can significantly enhance water storage efficiency, serving both practical and strategic needs in modern infrastructure.", "---", "For efficient water management, precise calculations of tank volume remain critical. Increasing radius offers a powerful lever to expand capacity in cylindrical storage systems, ensuring sustainable and scalable water supply solutions."]
