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A closed cylindrical tank contains 36pi cubic feet of water

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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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18 Aug 2015, 11:14
Extending the question - what if water is not half of the capacity or an easy number like 1/2 or 1/4 or 1/8. what is the shape of water when cylinder is placed on its side?
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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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03 May 2016, 08:39
Bunuel wrote:
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 water in the tank is 4 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

Notice that some editions of OG have a typo saying that the height of the water in the tank is 2 feet, it should read "the height of the water in the tank is 4 feet".

We are given 36pi occupies half the volume of the cylinder.
Now it does not matter in what orientation we keep the cylinder. half the volume will always occupy half the cylinder.
Now when cylinder is upright then half of its height is 4 feet bcz water occupies half the cylinder space. Refer to Bunuel's diagrams.
But when we place cylinder horizontal to the ground the diameter of the circle becomes the new height.
Now again the water should occupy half the cylinder space.
So it should occupy the radius length above the ground.
we know 1/2 pi*r^2*h=36 where h =8.
Hope this helps.
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A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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10 Jan 2017, 03:35
This is my approach.
Regardless of the shift of the cylinder the h (height) and r (radius) , will remain always the same.
V= 36π (volume of water when cylinder is filled in half capacity) --> so the max volume of the cylinder is 2 ∗36π =72π

Volume = π∗r^2∗h (The question asks for the radius in a confusing way) Here we have to notice that the new height = radius of cylinder ,so max volume is :
72π=π∗r^2∗8 (since its h= 4 feet when half capacity-->h=8 will be on full capacity)
72=8∗r^2
r^2=72/8
r^2=9
r= 3

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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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11 Jan 2017, 06:51
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Bunuel wrote:
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 water in the tank is 4 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

We are given that a closed cylindrical tank that is half full contains 36π cubic feet of water, and the height of the water is 4 feet. We can thus say that the full tank would have 72π cubic feet of water at a height of 8 feet. Using the volume formula, we can now determine the radius of the circular base:

volume = π(r^2)h

72π = π(r^2)(8)

9 = r^2

r = 3 feet

We see that the radius is 3 feet.

We need to determine the height of the water when the tank is placed on its side on level ground. When the cylinder is turned on its side, the diameter now represents the new height, and since the tank is half full, the new height of the water is equivalent to the radius, so the new height of the water is 3 feet.

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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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22 Feb 2017, 21:25
My OG - 2013 has a typo of height has "2"
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Joined: 09 Mar 2016
Posts: 1287
A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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28 Apr 2018, 08:04
Bunuel wrote:
SOLUTION

Notice that some editions of OG have a typo saying that the height of the water in the tank is 2 feet, it should read "the height of the water in the tank is 4 feet".

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 water in the tank is 4 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

Look at the diagram below:

Since the tank is half full when placed upright then naturally it'll also be half full when placed on its side, so the level of the water (when placed that way) will be half of the diameter, so $$r$$.

Now, given that $$V_{water}=\pi{*r^2}*H_{water}$$ --> $$36\pi=\pi{r^2}*4$$ --> $$r=3$$.

Bunuel hello -

"36pi cubic feet of water" doest it mean area is 36pi ?

I found this link and it has something similar but formula is hard to understand very complicated unlike yours https://www.mathopenref.com/cylindervolpartial.html

any difference between your formula method/ and the one described in the link ?

have a great weekend
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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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29 Jun 2018, 02:25
1
Volume of cylinder = pi*r^2*h = pi * r^2 * 4 ft = 36 pi
r^2= 9 pi
r=3ft
A cyl which is half full, placed on its side will also be filled up to half its height which is r.

Therefore, r = 3ft.
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Re: A closed cylindrical tank contains 36pi cubic feet of water &nbs [#permalink] 29 Jun 2018, 02:25

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