A cylindrical tank with a radius of 5 meters and a height of 10 meters is filled with water. If a sphere with a radius of 2 meters is fully submerged in the tank, by how much does the water level rise?

Sun, 03 May 2026 22:56:35 +0000

**How a cylindrical tank with a radius of 5 meters and a height of 10 meters responds when a 2-meter radius sphere is fully submerged—and what it means for water levels** Why are details about submerged objects in large cylindrical containers suddenly popping up in conversations online? From engineering forums to home improvement podcasts, curiosity is growing around everyday physical systems—especially large tanks used in water storage, industrial processes, and urban infrastructure. Among the most pressing questions is: if a solid sphere of 2 meters radius is fully submerged in a cylindrical tank with a 5-meter radius and 10-meter height filled with water, by how much does the water level rise? It’s a simple yet precise measurement—rooted in basic geometry—that reveals how volume displacement works. This isn’t just a math problem; it reflects real-world problem solving in engineering and design, where accurate volume calculations matter for safety, efficiency, and planning. The tank’s cylindrical shape means its volume depends solely on radius and height: V = πr²h. With a 5-meter radius and 10-meter height, the total volume is approximately 785.4 cubic meters (using π ≈ 3.14). The submerged sphere, with a radius of 2 meters, displaces an equal volume—about 33.51 cubic meters. Because the tank is already filled with water, this displaced water must rise around the submerged object, altering the water surface. Calculating exactly how much the water level climbs requires understanding displacement in related spatial geometry. Using standard formulas, the rise in water level (h) is found by dividing the sphere’s volume by the cross-sectional area of the tank’s circular base. The base area is π(5)² ≈ 78.54 square meters. Dividing 33.51 by 78.54 gives a rise of roughly 0.427 meters—or 42.7 centimeters. This subtle shift isn’t dramatic, but precise measurement supports infrastructure integrity, ensures proper capacity planning, and aids operational efficiency in industrial and public water systems.