GATE CSE 2024 | Set 2 | GA Question: 9

Question

​​​​A cube is to be cut into $8$ pieces of equal size and shape. Here, each cut should be straight and it should not stop till it reaches the other end of the cube.

The minimum number of such cuts required is

• A. $3$
• B. $4$
• C. $7$
• D. $8$

Comments

why not 7

Consider each cut as separate on each separate shape

first cut makes the cube into two separate cuboids, total cuts =1

next step we do 2 cuts cuts on two separate cuboids ,total cuts=3

next step we got 4 cuboids of same shapes, we do 4 cuts on each cuboid which makes total 8 identical cubes,total cuts =3+4=7

whenever we a cut on cube it will get separated, if its not get seperated at end of 3 cuts too we will get 8 identical cubes

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First two parallel cuts across the cube , now the cube is divided into 3 cubes

 Now Final cut is perpendcular to the previous two cuts , so now the cube is divided into 8 cubes.

Total cuts = 3

Answer 1

To cut a cube into 8 pieces of equal size and shape, you can achieve this with 3 cuts.

Here's how:

1. Make the first cut parallel to one face of the cube, dividing it into two equal halves.
2. Make the second cut perpendicular to the first cut, dividing the cube into four equal quarters.
3. Make the third cut perpendicular to both previous cuts, dividing each quarter into two equal parts.

After these three cuts, you will have 8 pieces of equal size and shape. So, the minimum number of cuts required is 3.

Comments

@Deepak Poonia Sir isn't the third cut which will be perpendicular to both cuts will be a diagonal cut, which is not allowed as only straight cuts are allowed, and also I think we cannot stack up the cube pieces and cut together, so will it not be the case that minimum cuts required will be 4?

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Assume a cube as 1 piece. Multiply it by 1/2 then again 1/2 then again 1/2, you get 1/8. that means 1 piece needs 3 cuts which can divide it equally. Its like (1/2)^3 = 1/8. This is mathematics, but without maths also just imagine a cube face and cut it perpendicularly to get 4 piece. Now cut it from another face of the cube just once which will be perpendicular to already before cut and you get 8 pieces. The cuts are always straight and never diagonal. Also I didn't get how without stacking cuts are possible. It's never said that stacking is not allowed.

Answer 2

3