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14 Jun 2012, 02:54
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
72% (02:11) correct
28%
(02:34)
wrong
based on 5152
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A closed cylindrical tank contains \(36\pi\) 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 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".
(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".
14 Jun 2012, 02:54
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Bookmarks
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 \(V_{water}=\pi{*r^2}*H_{water}\);
\(36\pi=\pi{r^2}*4\);
\(r=3\).
Answer: B.
Untitled.png [ 6.77 KiB | Viewed 48628 times ]
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 \(V_{water}=\pi{*r^2}*H_{water}\);
\(36\pi=\pi{r^2}*4\);
\(r=3\).
Answer: B.
Attachment:
Untitled.png [ 6.77 KiB | Viewed 48628 times ]
10 Feb 2014, 21:29
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Mackam1234
There are a few different relevant heights in the question:
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.
The height of the water in the tank is given to be 4 feet. Since the tank is filled to half its capacity, the height of the cylinder is 8 ft (though we don't need this).
Volume of the water \(= 36*\pi = \pi*r^2*4\)
r = 3
This is all we need to find the required height. Why? We know that the tank is filled to half its capacity. Imgine you have placed it on its side. If it were full of water, the height of the water in this position would be the diameter of the circular base (which is now the height). Since it is half full, the height of the water will come up to the mid point of the circle i.e. its radius. Since radius is 3, the height of water now will be 3 feet.
