#### 1201. A cylindrical tank with a radius of 5 meters and a height of 10 meters is filled with water. If half of the water is removed, what is the remaining volume of water in cubic meters? - Parker Core Knowledge

Understanding the Context

Imagine standing beside a large cylindrical tank, filled to the brim with water. With a radius of 5 meters and a height of 10 meters, this structure holds a significant amount of water—enough to fill over 800 bathtubs. But what happens when only half is removed? While the visual shift is striking, understanding the precise remaining volume reveals insights into fluid dynamics, measurement, and real-life applications. This puzzle isn’t just academic—it touches on infrastructure planning, industrial operations, and environmental efficiency. Those interested in water storage systems or fluid mechanics are increasingly exploring how tank configurations affect capacity and usage, making this a timely topic in US-focused discussions.

Why This Tank Size Matters for Modern Infrastructure

Cylindrical tanks are a common sight across the United States, used in agricultural irrigation, industrial processing, stormwater management, and commercial water supply. The dimensions you mentioned—radius 5 meters and height 10 meters—represent a classic configuration balancing space efficiency with capacity. As communities grow and demand for reliable water storage increases, understanding how volume behaves when portions are removed becomes essential. These calculations support smarter design, efficient resource use, and sustainable planning—especially as climate patterns emphasize precision in water distribution. For anyone analyzing tanks or working in water-related fields, mastering such fundamentals strengthens practical knowledge.

Key Insights

How Much Water Remains After Removing Half?

To find the remaining volume, start with the full cylindrical tank formula:
Volume = π × radius² × height
Plugging in the values:
Volume = π × (5)² × 10 = π × 25 × 10 = 250π cubic meters

With π approximately 3.1416, this equals about 785.4 cubic meters when filled completely. If half the water is removed, the remaining volume is simply half of that:
785.4 ÷ 2 ≈ 392.7 cubic meters

The exact value is 250π ÷ 2 = 125π cubic meters—a cleaner representation that reflects the mathematical precision without rounding for technical clarity.

Final Thoughts

Common Questions About Tank Capacity When Water is Reduced

H3: Is the remaining water still measured the same?
Yes.