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If a cube with the length of the side of 4 cm is cut into smaller cube

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If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

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New post Updated on: 04 Nov 2018, 02:56
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Question Stats:

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If a cube with the length of the side of 4 cm is cut into smaller cubes with the length of the side of 1 cm, then what is the percentage increase in the surface area of the resulting cubes?

A. 4%
B. 166%
C. 266%
D. 300%
E. 400%

Originally posted by Ansh10 on 03 Nov 2018, 23:52.
Last edited by Bunuel on 04 Nov 2018, 02:56, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

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New post 04 Nov 2018, 00:21
1
Surface area of larger cube = 6 * 4*4 = 96
No of cubes of 1cm each = 4*4*4 = 64
surface area of 64 small cubes = 64 * 6 * 1*1 = 384

% Inc = (384-96) 100 / 96
= 300%
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Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

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New post 04 Nov 2018, 02:57
Official Solution:

If a cube with the length of the side of 4 cm is cut into smaller cubes with the length of the side of 1 cm, then what is the percentage increase in the surface area of the resulting cubes?

A. 4%
B. 166%
C. 266%
D. 300%
E. 400%


A cube has 6 faces.

The surface area of a cube with the length of the side of 4 cm is \(6*4^2=6*16\) \(cm^2\).

Now, since the volume of the big cube is \(4^3=64\) \(cm^3\) and the volume of the smaller cubes is \(1^3=1\) \(cm^3\), then when the big cube is cut into the smaller cubes we'll get \(\frac{64}{1}=64\) little cubes. Each of those little cubes will have the surface area equal to \(6*1^2=6\) \(cm^2\), so total surface are of those 64 little cubes will be \(6*64\) \(cm^2\).

\(6*64\) is 4 times more than \(6*16\) which corresponds to 300% increase.

Or: general formula for percent increase or decrease, (percent change): \(\text{Percent} = \frac{\text{Change}}{\text{Original}}*100\)

So the percent increase will be: \(Percent=\frac{\text{Change}}{\text{Original}}*100=\frac{6*64-6*16}{6*16}*100=300%\).


Answer: D
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Re: If a cube with the length of the side of 4 cm is cut into smaller cube  [#permalink]

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New post 28 Dec 2018, 00:18
Hi Bunuel,

Requesting your support in clarifying the below query..

Questions :

a) A cube of side 3 cm is painted on all its sides. If it is sliced into 1 cubic centimeter cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

b) A cube of side 5 cm is painted on all its side. If it is sliced into 1 cubic centimer cubes, how many 1 cubic centimeter cubes will have exactly one of their sides painted?

Clarification Required :

a) For the first question , after slicing into 1 cm cubes .. How do we get 27 cubes in total ? Is it not 3*3 *6 = 54 (No. of sides)

b) Where as in the second question, the explanation provided had 25 * 6 = 150 cubes after slicing into 1cm cubes.

Please let me know how to find number of cubes per side after slicing
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Re: If a cube with the length of the side of 4 cm is cut into smaller cube   [#permalink] 28 Dec 2018, 00:18
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