Sat, 02 May 2026 09:02:18 +0000

A cylindrical tank with a radius of 5 meters is being filled with water at a rate of 2 cubic meters per minute. How long will it take to fill the tank to a height of 10 meters?
This real-world scenario reveals a steady, methodical process—and surprisingly precise math behind it. The tank’s volume determines the time needed, and even with a familiar shape, accurate calculations ensure efficiency in construction and water management projects across the U.S. Understanding the time required to fill large containers like this cylindrical tank hinges on volume and flow rate. With a radius of 5 meters, the tank’s base spans a circle of considerable area—785 square meters—creating space for significant water capacity. At two cubic meters flowing in every minute, the steady inlet rate shapes predictable fills, commonly seen in water storage and industrial applications. To determine how long it takes to reach a full 10-meter height, calculate the tank’s total volume. The volume of a cylinder is π × radius² × height. For a 5-meter radius and 10-meter height, that equals π × 25 × 10 = 250π cubic meters, approximately 785 cubic meters. At a steady inflow of 2 cubic meters per minute, dividing 785 by 2 reveals it takes roughly 392.5 minutes—just under seven hours—to fill to the target level. This process is not just routine—it’s vital for managing resources efficiently. Whether for agricultural irrigation, municipal water storage, or industrial processing, knowing fill times enables better planning and operational precision. The combination of consistent flow and predictable volume transforms abstract science into reliable scheduling.