what is the maximum number of identical pieces a cube can be cut into by 3 lines?

Answer 1

32 nos. if you use three different cutting methodes.
cutting through all 3-mid-points:
diagonal-1 and 2 mid-points.
diagonal-2 and 2 mid-points.
cutting through all 3-diagonals.

Answer 2

Identical pieces has to be a cube. If a side of a cube (square) is cut horizontally into three equal thirds, they make 3 rectangles. If they are cut vertically or in the opposite manner, they form 9 squares. Therefore 9 squares on each side makes 54.

Divide 54 by 2 as they form cubes and not squares
Therefore the answer is 27.

Answer 3

If the cube is cut into identical pieces by 3 parallel lines, the number of slices will be 4. If n is the number of lines cutting it, the number of pieces will be n+1.

If the cube is cut into pieces by 3 mutually perpendicular lines but the pieces are held together while cutting (like you hold a vegetable in your left hand and cut it with a knife held in right hand and rotate the vegetable cube so that the peieces are still held together), you will have 8 pieces.

Answer 4

Assuming you mean cutting the cute with 3 planes, I'm sure the answer is at least 8. Slicing it first through the middle in the north-south, second east-west, and third horizontally will cut the cube into 8 pieces. But you might get even more pieces if you angle the horizontal slice so that it cuts from corner to opposite corner...

Answer 5

Um.. cube is 3d, line is 2d. Line would not cut a cube into multiple pieces. It could poke an infinately small hole all the way through. If you used 3 lines to form a plane then you could cut a cube into 2 identical pieces.

Answer 6

8

Answer 7

let us think of a cube of side 3x cm
for convience let us assume that the cube is a cuboid with lenght,breadth,height equal to 3x cam each
given that we can cut the cube only thrice
first,we will cut lenght wise giving us 2 identical parts
second,we cut it breadthwise giving us 4 identical parts
third,we cut it heightwise to give us 8 identical parts
therefore we can cut in three different ways at the maximum and obtain 8 identical parts

Answer 8

A line cannot cut a cube into any separate pieces can it?

Answer 9

If you meant three lines of symmetry, then the maximum number of small identical pieces would be 8 along the three mutually perpendicular axes i.e., x,y,z.

Answer 10

you probabl;y mean by 3 planes , not lines..

for splitting with 3 planes

I only see 3 way to do that.
first one will give you 8 identical cubes pieces
( all planes through mid of cubeplane )

second way will give you 8 identical pyramides
all planes diagonally trough cubeplane

third way gives you also 8 kind of pyramides
one plane diagonally , other two planes through mid

Answer 11

3 lines if cut you get 9 out of it.