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When 8 steel cubes, each with edge of length 1 inch, are dropped into

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When 8 steel cubes, each with edge of length 1 inch, are dropped into [#permalink]

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New post 10 Dec 2017, 22:21
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When 8 steel cubes, each with edge of length 1 inch, are dropped into a cylindrical jar that is partially filled with water, the water level rises 1 inch, and water covers the eight cubes. A ninth steel cube with edge of length x inches is dropped into the jar, and the water rises another 1 inch, covering all nine cubes. What is the value of x?

(A) 8
(B) 6
(C) 4
(D) 3
(E) 2
[Reveal] Spoiler: OA

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When 8 steel cubes, each with edge of length 1 inch, are dropped into [#permalink]

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New post 10 Dec 2017, 22:35
Bunuel wrote:
When 8 steel cubes, each with edge of length 1 inch, are dropped into a cylindrical jar that is partially filled with water, the water level rises 1 inch, and water covers the eight cubes. A ninth steel cube with edge of length x inches is dropped into the jar, and the water rises another 1 inch, covering all nine cubes. What is the value of x?

(A) 8
(B) 6
(C) 4
(D) 3
(E) 2


Displacement of water caused by the 8 cubes with length 1 inch will be equal
to the displacement caused by the cube with length x inch.

This displacement of 1 inch water rising is caused by the change in volume
caused by the 8 cubes, which has a volume of \(1^3\) each.
The total change in volume is \(8*1^3 = 8\). For a similar displacement
to be caused by a cube of length x inch, the volume of this cube must be 8.

Therefore, \(x^3 = 8\) --> \(x = 2\)(Option E)
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Re: When 8 steel cubes, each with edge of length 1 inch, are dropped into [#permalink]

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New post 11 Dec 2017, 02:04
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Bunuel wrote:
When 8 steel cubes, each with edge of length 1 inch, are dropped into a cylindrical jar that is partially filled with water, the water level rises 1 inch, and water covers the eight cubes. A ninth steel cube with edge of length x inches is dropped into the jar, and the water rises another 1 inch, covering all nine cubes. What is the value of x?

(A) 8
(B) 6
(C) 4
(D) 3
(E) 2



Note:

Water level rises 1 inch in both cases and in both cases, all cubes are completely immersed. This means equal amount of water is displaced in both cases. Since water is displaced because of the volume of the cubes,

Volume of eight cubes = Volume of the ninth cube

8 * 1*1*1 = x*x*x

x = 2 inches
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Kudos [?]: 18479 [1], given: 237

Re: When 8 steel cubes, each with edge of length 1 inch, are dropped into   [#permalink] 11 Dec 2017, 02:04
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