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

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A large cube is made up of smaller equally sized cubes, where each sma  [#permalink]

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New post 30 Aug 2017, 15:22
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A large cube is made up of smaller equally sized cubes, where each smaller cube has sides \(\frac{1}{3}\) the length of the large cube. What approx % of the total volume is one of the small cubes?

A) 3

B) 3.7

C) 9

D) 11.11

E) 33.33
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Re: A large cube is made up of smaller equally sized cubes, where each sma  [#permalink]

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New post 30 Aug 2017, 17:12
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LakerFan24 wrote:
A large cube is made up of smaller equally sized cubes, where each smaller cube has sides \(\frac{1}{3}\) the length of the large cube. What approx % of the total volume is one of the small cubes?

A) 3

B) 3.7

C) 9

D) 11.11

E) 33.33


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:

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Re: A large cube is made up of smaller equally sized cubes, where each sma  [#permalink]

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New post 28 Jan 2019, 03:09
Sharing the algebraic way of working out this problem:

What is to be found: volume of 1 smaller cube/volume of larger cube [Assume as 1]
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)
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Re: A large cube is made up of smaller equally sized cubes, where each sma   [#permalink] 28 Jan 2019, 03:09
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