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

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-

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

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

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