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# A cube of side 5cm is painted on all its side. If it is sliced into 1

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A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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09 Jul 2007, 06:26
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A cube of side 5cm 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?

A. 9
B. 61
C. 98
D. 54
E. 64
[Reveal] Spoiler: OA
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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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09 Jul 2007, 06:31
trahul4 wrote:
A 5 cubic centimeter cube 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?

A. 9
B. 61
C. 98
D. 54
E. 64

D. 6*9=54. A cube has 6 sides, each of which has 9 cubes with one sides painted.
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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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09 Jul 2007, 06:33
trahul4 wrote:
A 5 cubic centimeter cube 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?

A. 9
B. 61
C. 98
D. 54
E. 64

9 such cubes for each of the 6 surfaces = 9 * 6 = 54 cubes. (D)
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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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09 Jul 2007, 07:26
Dear Wudy and Sumande

Please make the solution more clear.

First I don't understand how to get integer from 5 ^ 1/3 to get dimension of cube.

Also if you're talking about 9 cubes for every surface (3 x 3 x 3) and we're looknig for cubes with exactly one side painted that the solution is 6. One middle cube has only one painted side on every surface.
Or I didn't undertand the condition. Please explain.

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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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10 Jul 2007, 08:49
trahul4 wrote:
A 5 cubic centimeter cube 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?

A. 9
B. 61
C. 98
D. 54
E. 64

are you sure it's a 5 cubic centimeter cube or is it a 5 cubic metre cube?? there should be five 1 cubic centimeter cubes when a 5 cubic centimeter cube is cut up
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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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10 Jul 2007, 09:38
Andrey2010 wrote:
Dear Wudy and Sumande

Please make the solution more clear.

First I don't understand how to get integer from 5 ^ 1/3 to get dimension of cube.

Also if you're talking about 9 cubes for every surface (3 x 3 x 3) and we're looknig for cubes with exactly one side painted that the solution is 6. One middle cube has only one painted side on every surface.
Or I didn't undertand the condition. Please explain.

Well. I though the cube is 5*5*5 centimeter, or the question does not make sense-- how a 5 cubic centimeter cube is divided into 1 cubic centimeter cube?

The number listed above is how many faces painted for each 1cm*1cm cube on a surface.
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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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10 Jul 2007, 09:46
wudy wrote:
Andrey2010 wrote:
Dear Wudy and Sumande

Please make the solution more clear.

First I don't understand how to get integer from 5 ^ 1/3 to get dimension of cube.

Also if you're talking about 9 cubes for every surface (3 x 3 x 3) and we're looknig for cubes with exactly one side painted that the solution is 6. One middle cube has only one painted side on every surface.
Or I didn't undertand the condition. Please explain.

Well. I though the cube is 5*5*5 centimeter, or the question does not make sense-- how a 5 cubic centimeter cube is divided into 1 cubic centimeter cube?

The number listed above is how many faces painted for each 1cm*1cm cube on a surface.
32223
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32223

My assumption was exactly the same. I didn't think that a cube of side 5^(1/3) cm being divided into 1 cubic centimeter cubes makes sense. So, I assumed that each of the sides of the cube was 5 cm (a 5 cm cube as opposed to 5 cubic centimeter).
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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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10 Jul 2007, 21:19
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There is another way to do this problem. We know that all of the squares on each side have 2 sides (or 3 sides) painted. we want to remove them.

Make a new square which represents all of these squares. 5-2(one inch from each edge)=3

3.3=9 squares on each side.

9.6 sides is 54 squares
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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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30 Aug 2014, 16:54
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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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01 Sep 2014, 00:55
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trahul4 wrote:
A cube of side 5cm 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?

A. 9
B. 61
C. 98
D. 54
E. 64

Look at the image below:

Little cubes with exactly one painted side will be those 3*3=9, which are in the center of each face. (6 faces)*(9 per each) = 54.

Similar questions to practice:
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3-D Geometry Questions to practice: 3-d-geometry-questions-171024.html
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A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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10 Sep 2014, 20:14
Bunuel wrote:
trahul4 wrote:
A cube of side 5cm 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?

A. 9
B. 61
C. 98
D. 54
E. 64

Look at the image below:

Little cubes with exactly one painted side will be those 3*3=9, which are in the center of each face. (6 faces)*(9 per each) = 54.

Similar questions to practice:
the-entire-exterior-of-a-large-wooden-cube-is-painted-red-155955.html
a-big-cube-is-formed-by-rearranging-the-160-coloured-and-99424.html
64-small-identical-cubes-are-used-to-form-a-large-cube-151009.html
a-wooden-cube-whose-edge-length-is-10-inches-is-composed-of-162570.html
if-a-4-cm-cube-is-cut-into-1-cm-cubes-then-what-is-the-107843.html
a-large-cube-consists-of-125-identical-small-cubes-how-110256.html

3-D Geometry Questions to practice: 3-d-geometry-questions-171024.html

Hi Bunuel, When u show the image then i can quickly make out the answer and it gets very easy but this kind of 3-D accurate figure cant be drawn on paper and difficult to be thought in mind within 2 minutes. What should be done??

What is the best way to solve such questions?
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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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10 Sep 2014, 21:43
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snehamd1309 wrote:
Bunuel wrote:
trahul4 wrote:
A cube of side 5cm 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?

A. 9
B. 61
C. 98
D. 54
E. 64

Look at the image below:
Little cubes with exactly one painted side will be those 3*3=9, which are in the center of each face. (6 faces)*(9 per each) = 54.

Hi Bunuel, When u show the image then i can quickly make out the answer and it gets very easy but this kind of 3-D accurate figure cant be drawn on paper and difficult to be thought in mind within 2 minutes. What should be done??

What is the best way to solve such questions?

Not Bunuel, but lets try..

Refer diagram below; just imagine one side of the cube
Attachment:

cube.png [ 1010 Bytes | Viewed 7191 times ]

It will have 5 * 5 = 25 squares of 1 units

The border (the corner squares) will always be 2 side painted, so remaining are the pink shaded squares

There calculation per side = (5-2) * (5-2) = 3*3 = 9
(Two rows & two Columns are to be subtracted)

Total 6 sides = 9*6 = 54

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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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15 Sep 2014, 02:14
Shouldn't it ask " A cube of side 5cm is painted on all its faces"
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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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19 Oct 2015, 13:01
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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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22 Oct 2016, 00:29
Hello from the GMAT Club BumpBot!

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Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]

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22 Oct 2016, 02:21
Number of cubes 1 sides painted = 9 * 6 = 54

Additionally ,we can have the following as well

Number of cubes 2 sides painted = 12 * 3 = 36

Number of cubes 3 sides painted = 8
Re: A cube of side 5cm is painted on all its side. If it is sliced into 1   [#permalink] 22 Oct 2016, 02:21
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