Question**: A cylindrical tank with a radius of 3 meters is filled with water to a height of 10 meters. If the water is transferred to a cuboid tank with a base area of 45 square meters, what will be the height of the water in the cuboid tank? - Decision Point
How to Calculate Water Height After Transfer from a Cylindrical to a Cuboidal Tank: A Practical Problem
How to Calculate Water Height After Transfer from a Cylindrical to a Cuboidal Tank: A Practical Problem
When managing water storage systems, understanding how volume translates between different tank shapes is crucial. One common scenario involves transferring water from a cylindrical tank to a cuboid (box-shaped) tank. This article explains step-by-step how to calculate the water height in the cuboid tank when the original cylindrical tank holds water to a specified height.
Understanding the Context
Understanding the Problem
We begin with a cylindrical tank with:
- Radius ( r = 3 ) meters
- Height of water ( h_{\ ext{cyl}} = 10 ) meters
- Water transferred to a cuboid tank with base area ( A = 45 ) square meters
We need to find the final height of water ( h_{\ ext{cuboid}} ) in the cuboid tank.
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Key Insights
Step 1: Calculate the Volume of Water in the Cylindrical Tank
The volume ( V ) of a cylinder is given by the formula:
[
V = \pi r^2 h
]
Substituting the known values:
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[
V = \pi (3)^2 (10) = \pi \ imes 9 \ imes 10 = 90\pi \ ext{ cubic meters}
]
Using the approximation ( \pi pprox 3.1416 ):
[
V pprox 90 \ imes 3.1416 = 282.74 \ ext{ cubic meters}
]
Step 2: Relate Volume to Height in the Cuboid Tank
The cuboid tank has a base area (floor area) of ( 45 ) mÃÂò. The volume of water remains constant during transfer, so:
[
V = \ ext{Base Area} \ imes \ ext{Height}
]
[
90\pi = 45 \ imes h_{\ ext{cuboid}}
]
Solving for ( h_{\ ext{cuboid}} ):
[
h_{\ ext{cuboid}} = rac{90\pi}{45} = 2\pi
]
