SOLUTION: To cylindrical tanks sit side by side on a level surface. The first tank has a radius of 4 meters, a height of 10 meters, and is full of water. The second tank has a radius of 6 me

Algebra ->  Volume -> SOLUTION: To cylindrical tanks sit side by side on a level surface. The first tank has a radius of 4 meters, a height of 10 meters, and is full of water. The second tank has a radius of 6 me      Log On


   

Question 870421: To cylindrical tanks sit side by side on a level surface. The first tank has a radius of 4 meters, a height of 10 meters, and is full of water. The second tank has a radius of 6 meters, the height of 8 meters, and is empty. Water is pumped from the first tank to the second until the depth of water in both tanks is the same. What is the depth of water in each tank?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Two cylindrical tanks sit side by side on a level surface.
The first tank has a radius of 4 meters, a height of 10 meters, and is full of water.
The second tank has a radius of 6 meters, the height of 8 meters, and is empty.
Water is pumped from the first tank to the second until the depth of water in both tanks is the same.
What is the depth of water in each tank
Let h = the height of the water in both tanks
:
Find the original volume of water in first tank
V = pi%2A4%5E2%2A10
V = 502.655 cu/m
:
We know the total volume of the two tanks had to = 502.655 cu/m
Tank 1 vol + tank 2 vol = 502.655
pi%2A4%5E2%2Ah + pi%2A6%5E2%2A+h+=+502.655
factor out h
h%2816pi%2B36pi%29+=+502.655
add like terms
h%2852pi%29+=+502.655
divide by 52pi
h = 502.655%2F%2852pi%29
h = 3.077 meters will be the height in both tanks
:
:
:
See if that checks out; find the vol of each, should add up to 502.655
Tank1: pi%2A4%5E2%2A3.077 = 154.67 cu/m
Tank1: pi%2A6%5E2%2A3.077 = 348.00
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total volume both tanks: 502.67, close enough, don't you think