A cube of 3cm side is colored red on all of its six faces. It is cut intosmall cubes of side 1cm each. (a) No. of small cubes with 3 faces colored red (b) No. of small cubes with 2 faces colored red(c) No. of small cubes with 1 face colored red(d) No. of small cubes with no faces colored red

(a) No. of small cubes with 3 faces colored red : 8
(b) No. of small cubes with 2 faces colored red: 12
(c) No. of small cubes with 1 face colored red : 6
(d) No. of small cubes with no faces colored red: 1

Beena
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Sep 15th, 2005
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shashank

Nov 10th, 2005

hello, is there any formula of solving this type of questions or it is just on ur ?thanks

T.M.Arun kumar

May 12th, 2006

just imagine a cube
... 3 sided paintedis 8 (8 corner edges)
.... 2 sided paintded is 12
..... 1 side painted is 6( faces of cube)

udhay

Nov 21st, 2006

Formula for this is ;Total number of cubes = 27 i.e., 3 * 3 * 3 so take n=3Number of cubes with 1 side painted = (n-2) * (n-2) *6Number of cubes with 2 sides painted = (n-2) * 12Number of cubes with 3 sides painted = 8Number of cubes with no sides painted = 1

keerthi

Sep 18th, 2007

I got your formula but not able to understand why did u take n=3

is that to do with 3cm size

manojthesingham
Profile Answers by manojthesingham

Dec 4th, 2009

Extended CUBE sum
Here we cut Cubes into 3 equal parts on each side

n = 3,
  3faces=8;
  2faces=12;
  1faces=6;
  0faces=1;
n = 5,
  3faces=8x(5-2)^0;
  2faces=12x(5-2)^1;
  1faces=6x(5-2)^2;
  0faces=1x(5-2)^3;
n = 7,
  3faces=8x(7-2)^0;
  2faces=12x(7-2)^1;
  1faces=6x(7-2)^2;
  0faces=1x(7-2)^3
8;12;6;1; for 3 equal pieces
8;36;54;27; for 5 equal pieces
8;60;150;125; for 7 equal pieces.