The following questions are based on the information given below:
All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.
How many small cubes are there where one face is green and other one is either black or red ?
Number of small cubes having one face green and the other one is either red or black = 8 x 2 = 16
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The following questions are based on the information given below:
All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.
How many small cubes are there whose no faces are coloured ?
Number of small cubes having no face coloured = (x - 2)3
= (4 - 2)3
= 8
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The following questions are based on the information given below:
All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.
How many small cubes are there whose 3 faces are coloured ?
Number of small cubes having three faces coloured = 1 at each corner
= 1 x 8
= 8
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The following questions are based on the information given below:
All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.
How many small cubes are there whose only one face is coloured ?
Number of small cubes having only one face coloured = 4 from each face
= 4 x 6
= 24
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The following questions are based on the information given below:
All the opposite faces of a big cube are coloured with red, black and green colours. After that is cut into 64 small equal cubes.
How many small cubes are there whose at the most two faces are coloured ?
Number of small cubes having two faces coloured = 8 + 8 + 4 + 4 = 24
and Number of small cubes having only one face coloured = 4 x 6 = 24
and Number of small cubes having no face coloured = 4 + 4 = 8
Therefore, total number of small cubes whose at the most two faces are coloured = 24 + 24 + 8 = 56.
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A cube is cut in two equal parts along a plane parallel to one of its faces. One piece is then coloured red on the two larger faces and green on the remaining, while the other is coloured green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of same size and mixed up.
A cube is cut in two equal parts along a plane parallel to one of its faces. One piece is then coloured red on the two larger faces and green on the remaining, while the other is coloured green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of same size and mixed up.
What is the number of cubes with at least one green face each ?
A cube is cut in two equal parts along a plane parallel to one of its faces. One piece is then coloured red on the two larger faces and green on the remaining, while the other is coloured green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of same size and mixed up.
How many cubes have two red and one green face on each ?
A cube is cut in two equal parts along a plane parallel to one of its faces. One piece is then coloured red on the two larger faces and green on the remaining, while the other is coloured green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of same size and mixed up.
There is no such cube in all, where all the faces are unclosured.
Workspace
NA
SHSTTON
1
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Solv. In. Corr.
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10 / 10
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A cube is cut in two equal parts along a plane parallel to one of its faces. One piece is then coloured red on the two larger faces and green on the remaining, while the other is coloured green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of same size and mixed up.
How many cubes have each one red and another green ?
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