Question

What is the maximum number of identical pieces a cube can be cut into by 12 cuts?
Select one:
a. 125
b. 64
c. 115
d. 216

Answer 1

Answer:

125 is the answer of the ques.

Answer 2

a. 125

Dividing cube:

• The first cut will divide the cube into 2 parts.
• The second cut along the perpendicular direction will double the number of sections to 4
• Now the 3rd cut will also be in the perpendicular direction which will double 4 to 8 sections.
• So 8 cubes can be made in 3 cuts. All 3 pointers should be perpendicular to each other.
• Note that 1 cut = 2 parts cube, 2 cut = 3 pieces and so on.
• x cuts made near one plane cause x + 1 pieces.
• What makes sense behind this is, divide the given number of cuts into 3 equal parts and place the multiple cuts on each side perpendicular.
• To get the same pieces, the cuts should be made in accordance with the 3 planes of the cube.
• Let's make x, y, z cuts on all three planes so that (x + 1) (y + 1) (z + 1) = t maximum & x + y + z = 12.
• Different combinations are possible but t will be the limit in cutting (4, 4, 4).
• So the maximum pieces = (4 + 1) * (4 + 1) * (4 + 1) = 5 * 5 * 5 = 125.