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Cylindrical tank

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Cylindrical tank

by Sak32 » Tue Dec 03, 2013 2:18 am
A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the waer in the tank is 2 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

a) 2
b) 3
c) 4
d) 6
e) 9

What I don't get is why did we use height as equal to 4 since we are solving for the volume of water in the tank which is half filling it and it is given as equal to 2.
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by Mathsbuddy » Tue Dec 03, 2013 5:34 am
A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the waer in the tank is 2 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

Water volume:
pi * r^2 * h = 36 * pi
so r^2 * h = 36
Substitute water height h = 2 to get
r^2 = 18
so r = √18 = 3√2

[On it's side the water runs to full height which is double before, so H = 2h = 4 (but this is not needed in the question)].

As it is filled to half capacity, this means the water reaches the centre line (diameter) of the tank, which is at a height of the radius, r = 3√2 = 4.242640687...

So the closest answer is (C) 4
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by Sak32 » Tue Dec 03, 2013 7:17 am
The answer is B.
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by Mathsbuddy » Tue Dec 03, 2013 8:20 am
Sak32 wrote:The answer is B.
OK, let's try radius = 3:

Volume of water/pi = r^2 * 2h / 2 (half because it's half full)
Substitute r = 3 and h = 2

V/pi = 3^2 * 2 = 18

This is not 36.

Therefore. may I propose that the wording of the question is wrong.
Instead of "A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity", it should read "A closed cylindrical tank can contain 36pi cubic feet of water and is filled to half its capacity". Now the answer 3.

Otherwise, the question states that it actually contains 36pi cubic feet off water, and is half full - implying that the tank could contain 72pi cubic feet.
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by Mathsbuddy » Tue Dec 03, 2013 8:23 am
With the question re-worded to mean that the tank has 36pi capacity, which is only half full of water:

Water volume:
pi * r^2 * h = 18 * pi
so r^2 * h = 18
Substitute water height h = 2 to get
r^2 = 9
so r = √9 = 3
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by [email protected] » Tue Dec 03, 2013 11:33 pm
Hi All,

This question (it's from the OG13) has a typo in it (which has been publicly acknowledged). The prompt is SUPPOSED to state that "the height of the water in the tank is 4 feet." With that information, you should be able to solve the problem.

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Contact Rich at [email protected]
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by Mathsbuddy » Wed Dec 04, 2013 12:28 am
Using h=4

pi * r^2 * h = 36 * pi
so r^2 * h = 36
Substitute water height h =4 to get
r^2 = 9
so r = √9 = 3
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