PE 3 - Cubes | LR - Cubes

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Answer the following questions based on the information given below.

The faces of the cuboid are painted with three different colours - black, red, and yellow such that each colour is painted on at least one face. Now 4, 5 and 6 cuts are made in three different directions.

1. PE 3 - Cubes | LR - Cubes

What is the maximum possible number of smaller pieces that have only black on their faces?

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7 8 9 4 5 6 1 2 3 0 . -

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2. PE 3 - Cubes | LR - Cubes

What is the maximum possible number of smaller pieces that have only black and yellow painted on their faces?

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7 8 9 4 5 6 1 2 3 0 . -

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3. PE 3 - Cubes | LR - Cubes

What is the maximum number of smaller pieces with three colors painted on them, respectively?

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7 8 9 4 5 6 1 2 3 0 . -

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Answer the following questions based on the information given below.

A cube is painted using 3 different colors Red, Yellow and Green on three, two and one face respectively, such that no two faces with same color are opposite each other. The cube is then cut into 125 smaller but identical cubes.

4. PE 3 - Cubes | LR - Cubes

How many smaller cubes have exactly 2 colors on them?

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7 8 9 4 5 6 1 2 3 0 . -

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5. PE 3 - Cubes | LR - Cubes

How many smaller cubes have Red & Green but not Yellow on them?

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7 8 9 4 5 6 1 2 3 0 . -

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6. PE 3 - Cubes | LR - Cubes

How many smaller cubes do not have Red on them?

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7 8 9 4 5 6 1 2 3 0 . -

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7. PE 3 - Cubes | LR - Cubes

How many smaller cubes have exactly one color on them?

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7 8 9 4 5 6 1 2 3 0 . -

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Answer the following questions based on the information given below.

A cube is painted using 3 different colors such that each color is painted on exactly two opposite faces of the cube. Now this cube is cut into 210 smaller but identical pieces using minimum number of cuts.

8. PE 3 - Cubes | LR - Cubes

How many pieces have exactly two colors on them?

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7 8 9 4 5 6 1 2 3 0 . -

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9. PE 3 - Cubes | LR - Cubes

How many pieces have exactly one color on them?

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7 8 9 4 5 6 1 2 3 0 . -

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10. PE 3 - Cubes | LR - Cubes

A cube such that the number of colors on it is less than the number of its painted faces, is called an Ego-Cube. How many of the smaller cubes are Ego-Cubes?

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PE 3 - Cubes | LR - Cubes

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