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

Question

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

BrentGMATPrepNow · Accepted Answer

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...
 https://i.imgur.com/yFiyeUL.png

If we let   x   = the length of one edge of the ORIGINAL cube....
 https://i.imgur.com/o4D57KI.png

....then   x/2   = the length of one edge of the SMALLER cube....
 https://i.imgur.com/Uh1vYni.png

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

Luckisnoexcuse · Answer

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

Fdambro294 · Answer

I used the Ratio Method when comparing Similar Shapes

In the Case of Similar Cubes: If the RATIO of ---- Edge of a Smaller Cube : Edge of Original Cube = a : b
 Then the RATIO of ----- Volume of a Smaller Cube : Volume of Original Cube = a'3 : b'3

In this case, since 8 Similar Cubes are cut out of the Original Cube-

Ratio of: Vol. of a Smaller Cube : Vol. of Original Cube = 1 : 8
 and
 Ratio of: Edge of a Smaller Cube : Edge of Original Cube = {Cube Root of 1} : {Cube Root of 8}

Answer: 1 : 2

HinalAmin24 · Answer

Let's take A is side of original cube,
so volume = A^3 , which is given 72
If you will divide that into 8 cube the volume will be same.
Let's take "a" as a side of small cube, so volume will be a^3
therefore for cube = 8a^3

8a^3 =72
a^3 = 9

Question is ratio of smaller side to original side 
a^3 / A^3 = 9/72
a^3 / A^3 = 1/8
a/A = 1/2

chrtpmdr · Answer

Why is it wrong to first solve for the edges of the larger cube and then divide them through 8? This would lead to a ratio of 8:1. Trying to grasp the logic

happypuppy · Answer

Volume is irrelevant. 
If we cut it in 2 equal parts, vertically and horizontally, we get 8 cubes.
And each side is half the main side.
Hence, 1:2

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

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