Question

Three equi-dimensional cubes are joined face to face in a row and are coloured with
Blue on all faces. The first cube is cut into 8 equal pieces, middle one into 27 equal
pieces and last into 64 pieces.
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How many cubes have three faces coloured?
​

Answer 1

The nos. of cubes have three faces coloured are 8.

Step-by-step explanation:

Given:

The three equi-dimensional cuboid are joined  by face to face in a row and   are coloured with blue colour on  the all faces.

The 1st cuboid  is cut in 8 equal pieces, middle one is cut in 27 equal pieces and  last is cut  in 64 pieces.

To Find:

The nos. of cubes have three faces coloured

Formula Used:

The cubes which are at the vertices of the cuboid have three  coloured  faces.  Joined cuboid has  8 vertices .

Solution:

Three equi-dimensional cubes  are placed in a row  thus a cuboid  is formed having dimensions height :breadth: length=1:1:3.

Now, the exterior faces of the cuboid are painted blue.

Thereafter, the three cuboids were separated and cut into 8, 27 and 64 smaller cubes respectively .

There will be only 8 smaller cubes which will have their three sides painted blue  while they were part of the cuboid, before being separated and cut.

Thus, The number of cubes have three faces coloured are 8.

Answer 2

Answer:

There are eight coloured cubes, each with three faces.

Detailed explanation:

Given:

• The three equally sized cuboids are connected face to face in a row and have blue coloring on each face.

• The first cuboid is divided into 8 equal parts, the middle one into 27 pieces, and the last one into 64 pieces.

To Locate:

The number of cubes has three coloured faces.

The formula is:

The cubes at the cuboid's vertices have three different coloured faces. 8 vertices make up a joined cuboid.

Solution:

• Three identical cubes are arranged in a row, creating a cuboid with the dimensions 1:1:3 for height, width, and length.

• The cuboid's external faces are now blue in colour.

• The three cuboids were then split apart and divided into 8, 27, and 64 smaller cubes, respectively.

• There will only be eight smaller cubes, each of which had its three sides painted blue when it was a cuboid before being divided and chopped.

• Thus, there are 8 cubes with coloured faces on all three sides.

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