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The figure above shows water in a tank whose base is 2 feet by 6 feet.
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Updated on: 21 Feb 2021, 10:02
Updated on: 21 Feb 2021, 10:02
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The figure above shows water in a tank whose base is 2 feet by 6 feet. If a rectangular solid whose dimensions are 1 foot by 1 foot by 2 feet is totally immersed in the water, how many inches will the water rise?
(A) \(\frac{1}{6 }\)
(B) 1
(C) 2
(D) 3
(E) 12
Kudos for the right answer and explanation
The figure above shows water in a tank whose base is 2 feet by 6 feet.
[#permalink]
01 Feb 2021, 03:41
01 Feb 2021, 03:41
2
Hi,
I had a hard time solving this one(took me 5 mins to solve)
So, what I did was as we only have 2 dimensions for the tank, I considered the third one i.e. the height to be h feet.
Thus the Volume of the tank=lbh= 2*6*h=12h
Now the area of the rectangular solid=2*1*1=2feet
Hence, when we immerse this solid in the tank it will take the area of 2 feet. And the water, which was filled in the 2 feet will be raised.
Thus we need to find the height of the tank when the volume is 2 feet and the other dimensions being 2 &6
v=lbh
2=2*6*h
h=\(\frac{1}{6}\) feet
Please note we need final value in inches and not in feet.
12 inches=1 feet
So, \(\frac{1}{6}\) feet is 2 inches.
IMO C
I had a hard time solving this one(took me 5 mins to solve)
So, what I did was as we only have 2 dimensions for the tank, I considered the third one i.e. the height to be h feet.
Thus the Volume of the tank=lbh= 2*6*h=12h
Now the area of the rectangular solid=2*1*1=2feet
Hence, when we immerse this solid in the tank it will take the area of 2 feet. And the water, which was filled in the 2 feet will be raised.
Thus we need to find the height of the tank when the volume is 2 feet and the other dimensions being 2 &6
v=lbh
2=2*6*h
h=\(\frac{1}{6}\) feet
Please note we need final value in inches and not in feet.
12 inches=1 feet
So, \(\frac{1}{6}\) feet is 2 inches.
IMO C
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Re: The figure above shows water in a tank whose base is 2 feet by 6 feet.
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01 Feb 2021, 07:07
01 Feb 2021, 07:07
1
Carcass wrote:
Attachment:
GRE solid.jpg
The figure above shows water in a tank whose base is 2 feet by 6 feet. If a rectangular solid whose dimensions are 1 foot by 1 foot by 2 feet is totally immersed in the water, how many inches will the water rise?
(A) \(\frac{1}{6 }\)
(B) 1
(C) 2
(D) 3
(E) 12
Kudos for the right answer and explanation
To begin, let's say that the tank (with base dimensions of 2 feet by 6 feet) is EMPTY
Volume of rectangular solid = (length)(width)(height) = (1)(1)(2) = 2 cubic feet
Now "melt" the rectangular solid and pour it into the original tank.
Our goal is to find the height of this "liquid" in the tank
Let h = the height of the liquid in the tank
Since the volume must be preserved, it must be the case that (length)(width)(height) = 2
Plug in our values to get: (2)(6)(h) = 2
Solve to get: h = 1/6
Answer: A
