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A closed cylindrical tank contains 16 (pi) cubic feet of water

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A closed cylindrical tank contains 16 (pi) cubic feet of water [#permalink]

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New post 08 Oct 2014, 04:41
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A closed cylindrical tank contains 16 \(\pi\) cubic feet of water and is filled to one-quarter of its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is equal to the diameter of the tank’s base. What is the radius of the tank?

(A) 1

(B) 2

(C) \(2\sqrt{2}\)

(D) 4

(E) 8

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Re: A closed cylindrical tank contains 16 (pi) cubic feet of water [#permalink]

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New post 08 Oct 2014, 04:45
Gnpth wrote:
A closed cylindrical tank contains 16 \(\pi\) cubic feet of water and is filled to one-quarter of its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is equal to the diameter of the tank’s base. What is the radius of the tank?

(A) 1

(B) 2

(C) \(2\sqrt{2}\)

(D) 4

(E) 8


"Stolen" question from OG:
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

Discussed here: a-closed-cylindrical-tank-contains-36pi-cubic-feet-of-water-134500.html
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Re: A closed cylindrical tank contains 16 (pi) cubic feet of water [#permalink]

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New post 09 Feb 2015, 15:15
Gnpth wrote:
A closed cylindrical tank contains 16 \(\pi\) cubic feet of water and is filled to one-quarter of its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is equal to the diameter of the tank’s base. What is the radius of the tank?

(A) 1

(B) 2

(C) \(2\sqrt{2}\)

(D) 4

(E) 8



Total capacity = 64\(\pi\), which means that 16 \(\pi\) is 1/4th of the volume, which is \(\pi\)r^2*h/4. Therefore, \(\pi\)r^2*h/4=16\(\pi\). This leaves us with r^2*h=64 and h=64/r^2.

"When the tank is placed upright on its circular base on level ground, the height of the water in the tank is equal to the diameter of the tank’s base. What is the radius of the tank?" When the tank is placed upright, the height of water (1/4*h)=2r(diameter). Substituting for h we get, 1/4*64/r^2=2r. Solving for r we get r=2, which is answer B.
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Re: A closed cylindrical tank contains 16 (pi) cubic feet of water [#permalink]

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New post 01 Feb 2016, 19:30
volume is pi r^2 h
we have 16pi = pi r^2 * h
in this case, h = 2r or we have:
16 = r^2 * 2r or 16=2r^3.
r^3=8
r=2.
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Re: A closed cylindrical tank contains 16 (pi) cubic feet of water [#permalink]

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New post 25 Apr 2017, 05:56
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Re: A closed cylindrical tank contains 16 (pi) cubic feet of water   [#permalink] 25 Apr 2017, 05:56
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