Problems on Cubes

1. 64 smaller identical cubes are arranged to form a larger cube. How manysuch similar type of smaller identical cubes are required to completelycover the larger cubeNumber of smaller cubes with 3 faces open ?Number of smaller cubes with 2 faces open ?Number of smaller cubes with 1 faces open?Number of smaller cubes with 0 faces open?2. A cube is painted on all its faces with red color. The cube is now cut into343 smaller identical cubes?Number of smaller cubes with 3 faces open ?Number of smaller cubes with 2 faces open ?Number of smaller cubes with 1 faces open?Number of smaller cubes with 0 faces open?3. A cube is painted on 3 pairs of opposite faces with same color red, blue ,green . The cube is now cut into 216 smaller identical cubes?Number of smaller cubes with no red paint?Number of smaller cubes at least two different colors?Number of smaller cubes only red or only blue?Number of smaller cubes only red and blue?Number of smaller cubes with red and blue?

• A cube has 6 faces, 12 edges and 8 corners• Number of smaller cubes with 3 faces open = corners = 8• Number of smaller cubes with 2 faces open = 12 (n - 2)• Number of smaller cubes with 1 faces open = 6• Number of smaller cubes with 0 faces open =

64 smaller identical cubes are arranged to form a larger cube.Number of smaller cubes with 3 faces open ?Number of smaller cubes with 2 faces open ?Number of smaller cubes with 1 faces open?Number of smaller cubes with 0 faces open?

1.

Ans:=> n = 4Number of smaller cubes with 3 faces open = 8Number of smaller cubes with 2 faces open = 12 (4 - 2) = 24Number of smaller cubes with 1 faces open = 6 ଶNumber of smaller cubes with 0 faces open = ଷ= 8

A cube is painted on all its faces with red color. The cube is now cut into 343smaller identical cubes?

Number of smaller cubes with 3 faces open ?Number of smaller cubes with 2 faces open ?Number of smaller cubes with 1 faces open?Number of smaller cubes with 0 faces open?

2.

Ans:=> n = 7Number of smaller cubes with 3 faces open = 8Number of smaller cubes with 2 faces open = 12 (7 - 2) = 60Number of smaller cubes with 1 faces open = 6 ଶ 150Number of smaller cubes with 0 faces open = ଷ= 125

A cube is painted on 3 pairs of opposite faces with same color red, blue ,green . The cube is now cut into 216 smaller identical cubes?

Number of smaller cubes with no red paint?Number of smaller cubes at least two different colors?Number of smaller cubes only red or only blue?Number of smaller cubes only red and blue?Number of smaller cubes with red and blue?

3.

Ans :n = 6Number of smaller cubes with no red paint = 144Number of smaller cubes at least two different colors = 56Number of smaller cubes only red or only blue = 64Number of smaller cubes only red and blue = 16Number of smaller cubes with red and blue = 24

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Problems for practice are given in the description of the video.

Practice problemson Cubes

1. A cube is painted on 3 pairs of adjacent faces with same color red, blue,green. This cube is now cut into 216 smaller identical cubes

Number of smaller cubes with no red paint?Number of smaller cubes at least two different colors?Number of smaller cubes only red or only blue?Number of smaller cubes only red and blue?Number of smaller cubes with red and blue?

2. A cube is painted on 3 faces with 3 different colors red, green and blue.This cube is cut into 343 identical cubes.

Number of smaller cubes painted?Number of smaller cubes with 3 faces painted ?Number of smaller cubes with 2 faces painted?Number of smaller cubes with 1 faces painted?Number of smaller cubes with 0 faces painted?

1. A cube is painted on 3 pairs of adjacent faces with same color red, blue,green. This cube is now cut into 216 smaller identical cubesNumber of smaller cubes with no red paint?Number of smaller cubes at least two different colors?Number of smaller cubes only red or only blue?Number of smaller cubes only red and blue?Number of smaller cubes with red and blue?

Ans :n = 6Number of smaller cubes with no red paint = 72Number of smaller cubes at least two different colors = 44Number of smaller cubes only red or only blue = 72Number of smaller cubes only red and blue = 14Number of smaller cubes with red and blue = 18

2. A cube is painted on 3 faces with 3 different colors red, green and blue.This cube is cut into 343 identical cubes.Number of smaller cubes painted?Number of smaller cubes with 3 faces painted ?Number of smaller cubes with 2 faces painted?Number of smaller cubes with 1 faces painted?Number of smaller cubes with 0 faces painted?

Ans: n = 7Number of smaller cubes painted = 43Number of smaller cubes with 3 faces open = 1Number of smaller cubes with 2 faces open = 18Number of smaller cubes with 1 faces open = 75Number of smaller cubes with 0 faces open = 300

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