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metallicafan
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15 Feb 2012, 09:08
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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69% (01:52) correct
31%
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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
Source: Jeff Sackmann problems - https://www.gmathacks.com
(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
Source: Jeff Sackmann problems - https://www.gmathacks.com
15 Feb 2012, 09:21
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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
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
15 Feb 2012, 10:26
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metallicafan
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.
