Reasoning :: Cubes,Venn Diagram And Puzzles :: Cubes

• Cubes,Venn Diagram And Puzzles - Cubes
• Cubes,Venn Diagram And Puzzles - Venn Diagram
• Cubes,Venn Diagram And Puzzles - Puzzles

216 samm identical cubes are arranged to form a large cube.Now three faces of the largecubes are painted yellow, of which no two faces are opposite each other.Of the remaining faces, two are painted green and the other black.

How many Small cubes have exactly two colors on them?

Answer:

Explanation:

Here , $n^{3}=216 \Rightarrow n=6$

Corners(8)

Edges(12)

Faces(6)

At corners ,5 caubes have exactly 2 colors.

On the edges(n-2)8 cubes have exactly two colors=32 cubes

$\therefore Total number of cubes=37$

A cube , painted on all its faces, is cut into 125 identicalsmaller cubes.

How many smaller cubes have no face painted ?

Answer:

Explanation:

Here $n^{3}=125$

$\Rightarrown=5$

Cubes with two faces painted:12(n-2)=12(3)=36

What is the minimum number of cuts required to cut a cube into 24 identical pieces?

Answer:

Explanation:

24=2\times 3\times 4 =(1+1)2+1)(3+1)

$\therefore1+2+3=6$ cuts are required.

A large cube is formed using 125 identical smaller cubes and is placed at the corner of a large room.How many such smaller cubes are required to cover the large cube completely, so that the figure obtained also must be a cube?

Answer:

Explanation:

Number of cubes required $=(5+1)^{3}-5^{3}$

$=91$

If two,three and four cuts are made parallel to different faces of cube, then what is the number of identical pieces obtained?

Answer:

Explanation:

$(2+1)\times (3+1)\times (4+1)$$ =3\times 4\times 5$$=60$ 

• Cubes,Venn Diagram And Puzzles - Cubes
• Cubes,Venn Diagram And Puzzles - Venn Diagram
• Cubes,Venn Diagram And Puzzles - Puzzles