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A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]
09 Jul 2007, 06:26

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Difficulty:

45% (medium)

Question Stats:

67% (02:16) correct
33% (02:00) wrong based on 150 sessions

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?

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]
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.
32223
21112
21112
21112
32223

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

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

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

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

Thank you in advance.

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
21112
21112
21112
32223

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

Thank you in advance.

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 21112 21112 21112 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).

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]
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]
01 Sep 2014, 00:55

1

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Expert's post

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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.

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

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??

Re: A cube of side 5cm is painted on all its side. If it is sliced into 1 [#permalink]
10 Sep 2014, 21:43

1

This post received KUDOS

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.

Answer: D.

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 2022 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)

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