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A closed cylindrical tank contains 20*(pi) cubic feet of

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A closed cylindrical tank contains 20*(pi) cubic feet of [#permalink]

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New post 15 Feb 2012, 09:08
3
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

68% (01:29) correct 32% (01:58) wrong based on 140 sessions

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A closed cylindrical tank contains 20*(pi) 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 5 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?
(Note: "pi" is the constant to calculate the area in a circle. Does someone know its code in the keyboard?)

(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3

Enjoy it as much as I did 8-)

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Re: Beautiful question - Just common sense! [#permalink]

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New post 15 Feb 2012, 09:21
1
Answer should be C. 2

Half the capacity \(=20{\pi}\) cubic feet
So Full Capacity \(=40{\pi}\) cubic feet

Half the Length \(=5\) feet
So Full Length \(=10\) feet

Volume of Cylinder \(={\pi}r^2h\)
\(h=10\)
So \({\pi}r^2h=40{\pi}\)
So \({\pi}r^2*(10)=40{\pi}\)
So \(r^2=4\)
So \(r=2\)

Lying on the ground, water should be half the way up the cylinder, since the cylinder is half full so technically it is as high above the ground as the radius which is \(2\)

Hence C
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Re: A closed cylindrical tank contains 20*(pi) cubic feet of [#permalink]

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New post 15 Feb 2012, 10:26
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metallicafan wrote:
A closed cylindrical tank contains 20*(pi) 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 5 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?
(Note: "pi" is the constant to calculate the area in a circle. Does someone know its code in the keyboard?)

(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3

Enjoy it, just as I did 8-)

Source: Jeff Sackmann problems - http://www.gmathacks.com


Since the tank is half full when placed upright then it will also be half full when placed on its side, so the level of the water will be half of the diameter, so r.

Now, given that \(V_{water}=\pi{*r^2}*H_{water}\) --> \(20\pi=\pi{r^2}*5\) --> \(r=2\).

Answer: C.
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Re: A closed cylindrical tank contains 20*(pi) cubic feet of [#permalink]

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New post 05 Mar 2017, 22:59
metallicafan wrote:
A closed cylindrical tank contains 20*(pi) 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 5 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?
(Note: "pi" is the constant to calculate the area in a circle. Does someone know its code in the keyboard?)

(A) 1
(B) 1.5
(C) 2
(D) 2.5
(E) 3

Enjoy it as much as I did 8-)

Source: Jeff Sackmann problems - http://www.gmathacks.com


Alt + 227 is the code for Pi. :)
Re: A closed cylindrical tank contains 20*(pi) cubic feet of   [#permalink] 05 Mar 2017, 22:59
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