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? - Deep Underground Poetry
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:
🔗 Related Articles You Might Like:
📰 This SEISSELLING Basketball Court Steals the Show – Here’s Why Everyone’s Obsessed! 📰 Top 5 Basketball Courts That Will Make You Want to Dribble Every Day – SPOILER: It’s Not Just Any Court! 📰 From Backyard Dreams to Pro-Level Courts – Here’s the Basketball Court Anyone’s Been Hunting! 📰 How A Gaul Creates The Ultimate Chewbacca Sound Wow Its Unreal 4924106 📰 The Giant Backpack That Double Your Survival Chances In Minecraft 5942751 📰 Bebop And Rocksteady 169100 📰 Radisson Hotel Lenexa Overland Park 5859649 📰 Hhs Data Breach Page 8631388 📰 7 Zip Download 5955726 📰 Dont Miss This How 401K Lending Strategies Are Boosting Millions Retirement Balance 8859241 📰 Water Filter Sediment 1392135 📰 You Wont Believe How Addictive Tic Tac Toe Game Istry It Now 102152 📰 Sesa Sterlite Share Price 4641279 📰 Meaning Of Berthed 5328208 📰 Trapped In Bad Seating This Club Chair Is A Game Changer You Need Now 9400667 📰 Unlock The Ultimate Epic Experienceplay Superhero Games Online Tonight 9340271 📰 Hells Kitchen Minneapolis 2990551 📰 Collins Street Bakery 8518022Final 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 ) 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
]
