A large cube is made up of smaller equally sized cubes, where each

Question

A large cube is made up of smaller equally sized cubes, where each smaller cube has sides 1/3 the length of the large cube. What approximate percent of the total volume is one of the small cubes?

(A) 3
(B) 3.7
(C) 9
(D) 11.11
(E) 33.33

BrentGMATPrepNow · Accepted Answer

Let the large cube have sides with length 3
This means the volume of the large cube = (3)(3)(3) =  27

This means a small cube will have sides with length 1
So, the volume of the small cube = (1)(1)(1) =  1

What approx % of the total volume is one of the small cubes?  
We need to convert  1 / 27   to a percent. 
NOTICE that 1/25 = 4%
So,  1 / 27   to a percent will be a little bit smaller than 4%
Only one answer choice meets that condition.

Answer:  B

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Pritishd · Answer

Sharing the algebraic way of working out this problem:

What is to be found: volume of 1 smaller cube/volume of larger cube  
Lets say the side of the larger cube is x, then as per the question stem the side of the smaller cube is x/3.

Now we know that the volume of a cube with side L is L*L*L. Using the same here and plugging values into 1:

=(x/3)*(x/3)*(x/3) / x*x*x
all the x's cancel out leaving (1/3)*(1/3)*(1/3)=1/27 or 0.0363
converting to percent yields 3.63% ~ closest to option B (Ans. Option B)

Fdambro294 · Answer

Concept: when we are given the Ratio of Side Lengths of a 2-D Figure, for Example a Square, the Ratio of the Areas is the SQUARE of the Ratio of the Side Lengths

For Example:

Side of Square A = 1x

Side of Square B = 3x

Area of Square A in Ratio Units = (1x) * (1x) = 1(x^2)
________________________________________________
Area of Square B in Ratio Units = (3x) * (3x) = 9(x^2)

Canceling the Unknown Ratio Multiplier:

Ratio of: Area of Square A / Area of Square B = 1 / 9

BUT, in cases of 3-D Figures:

(1st) Every Cube is, by definition, similar to Every Other Cube

(2nd) when we Find the Volume of a Cube, we take the Length of the Edge and CUBE it

thus, the Rule for 3-D Figures:

Given the Ratio of Edges of 2 Similar Cubes is = a : b

then the Ratio of the Volumes of the 2 Similar Cubes is = (a)^3 : (b)^3

In this Question:

Each Smaller Cube has an Edge = (1/3) * (Edge of ENTIRE Larger Cube)

thus:

Ratio of: (Edge of Smaller Cube) : (Edge of Larger Cube) = 1 : 3

Ratio of: (VOLUME of Smaller Cube) : (VOLUME of Larger Cube) = (1)^3 : (3)^3 = 1 : 27

1/27 is equal to approximately = .037

Percent = 3.7%

-B-

Alternative Method:

If you draw out the figure and make the Entire Large Cube with an Edge = 3

You can then Divide the Larger Cube into smaller Cubes with Edge = 1

You will see that there are 3 Stacks of 9 Smaller Cubes that will make up the Entire Larger Cube

(3) * (9) = 27 Cubes

Any 1 of these Cubes will be (1/27) of the Entire Figure

1/27 = .037 = 3.7%

-B-

nkr037 · Answer

Let's say the side of the larger cube is 3
So, side of each of the smaller cubes in it is one-third of 3, which is 1
Volume of a cube is s*s*s 
Volume of larger cube= 3*3*3= 27
Volume of smaller cube = 1*1*1 = 1
% of total volume of one of the smaller cube to the larger cube is: 1/27

Convert 1/27 to decimal:  
27*4 = little more than 100
1*4 = 4
4/100 is 4%
4/something more than 100 should be a little less than 4%
Only option to satisfy that is  Option B - 3.7

yuxiangdreamMBA · Answer

The question is not clear, as it said "total volume" so you also should add all the volumes of the 9 small cubes inside the large cube

bumpbot · Answer

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A large cube is made up of smaller equally sized cubes, where each

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