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? - Malaeb
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.
Image Gallery
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:
๐ Related Articles You Might Like:
๐ฐ How Do I Cancel My Microsoft Office 365 Subscription ๐ฐ How Do I Cancel My Microsoft Subscription ๐ฐ How Do I Cancel Xbox Game Pass ๐ฐ Dimensions Are 8 Meters By 19 Meters 5425730 ๐ฐ El Misterio Del Tiempo Paralizado En Lilburn Comprueba Esto Ahora 9604702 ๐ฐ Auto Ins Co Ratings 834220 ๐ฐ You Wont Believe These 11 Themes That Will Transform Your Win 11 Experience 7696413 ๐ฐ Georgian Court Lakewood 6244637 ๐ฐ Activate Phone On Verizon 8370932 ๐ฐ Screen Record On Mac With Audio 7729519 ๐ฐ Permissions Declaration Form 5318414 ๐ฐ Hotel Regina Barcelona 1417963 ๐ฐ Excel Macros 1692076 ๐ฐ Online Games That Are Good 7818056 ๐ฐ Barry White Never Never Gonna 9315370 ๐ฐ You Wont Believe What Happened In Super Mario Logans Latest Challenge 955787 ๐ฐ Claudeai 9815200 ๐ฐ Permit Practice Test Georgia 8218288Final Thoughts
[
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 ) mรยรยรยรยฒ. 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
]
