A cylindrical tank with a radius of 3 meters is filled with water to a height of 4 meters. If the water is transferred to a tank with double the radius but the same height, what will be the new height of the water?
["# How Upgrading a Cylindrical Tank Affects Water Volume: A Practical Example", "When managing water storage in industrial or residential settings, understanding how tank dimensions affect volume is crucial. This article explores a real-world scenario involving a cylindrical water tank and how changing its size impacts water capacity — specifically, what happens when transferring water from one tank to another with different radius and height.", "### The Initial Setup: A Standard Cylindrical Tank", "Consider a cylindrical tank with a radius of 3 meters, filled with water to a height of 4 meters. To determine the current volume of water, we apply the formula for the volume of a cylinder:", "[ V = \pi r^2 h ]", "Where:\n- ( r = 3 , \ ext{meters} )\n- ( h = 4 , \ ext{meters} )", "Plugging in the values:", "[ V = \pi \ imes (3)^2 \ imes 4 = \pi \ imes 9 \ imes 4 = 36\pi , \ ext{cubic meters} ]", "This means the tank initially holds 36π cubic meters of water.", "### The New Tank: Double the Radius, Same Height", "The transferred water is moved to a new tank that maintains the same height of 4 meters, but now has double the radius, so:", "- New radius = ( 2 \ imes 3 = 6 , \ ext{meters} )\n- Height remains = ( 4 , \ ext{meters} )", "Calculating the volume of the new tank using the same formula:", "[ V_{\ ext{new}} = \pi \ imes (6)^2 \ imes 4 = \pi \ imes 36 \ imes 4 = 144\pi , \ ext{cubic meters} ]", "### Comparing Volumes and Calculating New Water Height", "The original volume was ( 36\pi , \ ext{m}^3 ), and the new tank can hold ( 144\pi , \ ext{m}^3 ). Since we transfer only the water originally in the 3-meter radius tank, the amount of water remains ( 36\pi , \ ext{m}^3 ), but it now occupies a larger tank with greater capacity.", "To find the new water height in the larger tank, rearrange the volume formula to solve for height (( h_{\ ext{new}} )):", "[ h_{\ ext{new}} = \frac{V}{\pi r^2} = \frac{36\pi}{\pi \ imes 6^2} = \frac{36\pi}{\pi \ imes 36} = 1 , \ ext{meter} ]", "### Conclusion", "Despite the increased tank size — doubling the radius from 3 meters to 6 meters — and keeping the same volume of water, the water level only reaches 1 meter in the new tank, not the full 4 meters. This demonstration highlights a key principle: increasing tank cross-sectional area reduces water height for a fixed volume.", "For engineers and facility managers, this illustrates the importance of understanding how tank dimensions directly influence water storage efficiency. Choosing the right dimensions ensures optimal space utilization and prevents underutilized height or overflow risks.", "In summary: When a cylindrical tank with a 3-meter radius and 4-meter water height transfers water to a tank with double the radius (6 meters) but the same 4-meter height, the water fills only 1 meter of the new tank — even though the tank can hold significantly more water."]
