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A cube of side 7 cm is coloured on pair of opposite faces by

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A cube of side 7 cm is coloured on pair of opposite faces by  [#permalink]

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New post 04 Nov 2013, 22:31
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A
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C
D
E

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Question Stats:

60% (02:18) correct 40% (02:20) wrong based on 245 sessions

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A cube of side 7 cm is coloured on pair of opposite faces by Red, Green and Yellow shades. The cube is then cut into unit cubes. How many of the unit cubes will have exactly two coloured faces?

A) 150
B) 125
C) 60
D) 49
E) 40
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Re: A cube of side 7 cm is coloured on pair of opposite faces by  [#permalink]

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New post 05 Nov 2013, 00:45
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b2bt wrote:
A cube of side 7 cm is coloured on pair of opposite faces by Red, Green and Yellow shades. The cube is then cut into unit cubes. How many of the unit cubes will have exactly two coloured faces?

A) 150
B) 125
C) 60
D) 49
E) 40


Look at the figure below:
Attachment:
Untitled.png
Untitled.png [ 67.67 KiB | Viewed 4797 times ]
Only the edge cubes marked with dots will have exactly two colored faces. 5 cubes per edge * 12 edges = 60 cubes.

Answer: C.

Hope it's clear.

P.S. A cube has 12 edges. There are 4 edges on the top square, 4 on the bottom square and 4 more that connect the 2 squares.
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Re: A cube of side 7 cm is coloured on pair of opposite faces by  [#permalink]

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New post 09 Sep 2017, 07:47
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Perfectly explained by Bunuel.
Just wanted to add few more points to solve such questions quickly.

Below are the formulae that can be used to find different number of cubes colored:
For a cube:
Number of cubes with 0 side painted= (n-2) ^3
Number of cubes with 1 sides painted =6(n - 2) ^2
Number of cubes with 2 sides painted= 12(n-2)
Number of cubes with 3 sidess painted= 8(always)

Thanks
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A cube of side 7 cm is coloured on pair of opposite faces by  [#permalink]

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New post 30 Sep 2019, 19:51
devanshu92 wrote:
Perfectly explained by Bunuel.
Just wanted to add few more points to solve such questions quickly.

Below are the formulae that can be used to find different number of cubes colored:
For a cube:
Number of cubes with 0 side painted= (n-2) ^3
Number of cubes with 1 sides painted =6(n - 2) ^2
Number of cubes with 2 sides painted= 12(n-2)
Number of cubes with 3 sidess painted= 8(always)

Thanks


Hi devanshu92 and bunuel, can you please elaborate more on the above formula? What does n stand for? Is that n= length of side?
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A cube of side 7 cm is coloured on pair of opposite faces by   [#permalink] 30 Sep 2019, 19:51
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