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A cube has a volume of 72. If it is divided into 8 equal cubes, the

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A cube has a volume of 72. If it is divided into 8 equal cubes, the [#permalink]

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New post 06 Dec 2017, 03:19
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A cube has a volume of 72. If it is divided into 8 equal cubes, the ratio of an edge of a smaller cube to an edge of the original cube is

(A) 1 : 2
(B) 1: 3
(C) 1 : 3√2
(D) 2 : 9
(E) 1 : 9
[Reveal] Spoiler: OA

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A cube has a volume of 72. If it is divided into 8 equal cubes, the [#permalink]

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New post 06 Dec 2017, 03:42
Bunuel wrote:
A cube has a volume of 72. If it is divided into 8 equal cubes, the ratio of an edge of a smaller cube to an edge of the original cube is

(A) 1 : 2
(B) 1: 3
(C) 1 : 3√2
(D) 2 : 9
(E) 1 : 9


Volume of each small cube = 72/8 = 9
Edge of each small cube = 9^1/3
Edge of Original cube = 72^1/3
\((9^(1/3)) / (8^(1/3)) * (9^(1/3))\)
1/2
A
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Re: A cube has a volume of 72. If it is divided into 8 equal cubes, the [#permalink]

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New post 06 Dec 2017, 09:17
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Top Contributor
Bunuel wrote:
A cube has a volume of 72. If it is divided into 8 equal cubes, the ratio of an edge of a smaller cube to an edge of the original cube is

(A) 1 : 2
(B) 1: 3
(C) 1 : 3√2
(D) 2 : 9
(E) 1 : 9


Great question!
The great thing about it is that the volume of the original cube is irrelevant.
It all comes down to what happens when we divide ANY cube into 8 equal cubes.
Here's what I mean.

Take a cube and divide it into 8 equal cubes...
Image

If we let x = the length of one edge of the ORIGINAL cube....
Image

....then x/2 = the length of one edge of the SMALLER cube....
Image

What is the ratio of an edge of a smaller cube to an edge of the original cube?
Get get: x/2 : x
Divide both sides by x to get the EQUIVALENT ratio: 1/2 : 1
Multiply both sides by 2 to get the EQUIVALENT ratio: 1 : 2

Answer: A

Cheers,
Brent
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Re: A cube has a volume of 72. If it is divided into 8 equal cubes, the   [#permalink] 06 Dec 2017, 09:17
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