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655-705 Level|   Geometry|      
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A cube of side 7 cm is coloured on pair of opposite faces by 04 Nov 2013, 22:31
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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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C
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A cube of side 7 cm is coloured on pair of opposite faces by 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)

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A cube of side 7 cm is coloured on pair of opposite faces by 05 Nov 2013, 00:45
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b2bt
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
Show more

Look at the figure below:
Attachment:
Untitled.png
Untitled.png [ 67.67 KiB | Viewed 18467 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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A cube of side 7 cm is coloured on pair of opposite faces by 30 Sep 2019, 19:51
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devanshu92
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
Show more

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 22 Nov 2019, 16:37
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hanvd1990
devanshu92
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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hanvd1990 nstands for the number of cubes formed . In this case the side is 7 and the cube is cut into unit cubes hence n=7
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A cube of side 7 cm is coloured on pair of opposite faces by 05 Sep 2021, 23:48
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Total edges in cube = 12

The corner most cubes on an edge have three faces painted. So out of all cubes on edges, take the 2 cubes out.

Since its side is 7cm and it is cut into a unit cube that means there are 7 cubes on 1 edge and we will take 2 cubes out: 7 - 2 = 5.

Total cubes with 2 face painted = 12 * 5 = 60

Answer C
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A cube of side 7 cm is coloured on pair of opposite faces by 16 Feb 2022, 12:40
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Hi,
from the given data that the original cube has side = 7cm, how can we know that each unit cube is 1x1x1 cm? assuming 7cm = 7units? :?

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A cube of side 7 cm is coloured on pair of opposite faces by 14 Oct 2022, 09:41
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Bunuel
b2bt
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
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.
Show more

Hi Bunuel
What about the cubes in the middle? Why didnt we consider them?
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A cube of side 7 cm is coloured on pair of opposite faces by 21 Oct 2023, 04:53
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