cubes

Question

1)if six cuts are made to cube what isax no of pieces obtained?

2)if 10 cuts are made on cube what is max no of pieces obtained?

3)what is min no of cuts to obtain 216 identical pieces?

4)what is min no of cuts required to cut cube in 24 pieces?

5)27 identical cubes are aranged to form larger cube.How many such cubes are required to completely cover larger cube so that figure obtained is also cube?

1)125 2)98 3)80 4)64

Answer 1

1) 6 cuts , calculate Maximum pieces so  2 cut in X directions give 3 pieces , 2 cuts in Y direction give 3 pieces , 2 cuts in Z directions give 3 pieces so total pieces = 3*3*3= 27

2) similar when 10 cuts  means cuts in (X,Y,Z)= (4,3,3) 

so no of pieces maximum = (4+1)(3+1)(3+1) = 80 pieces ...

3) 216 pieces with minimum cuts so it required cuts in X,Y,Z all directions ... 

 216= 6*6*6 = (5+1)(5+1)(5+1) = 5+5+5 =15 cuts which is minimum ...

4) similar as 3 one . 24= 2*3*4=(1+1)(2+1)(3+1) = 1+2+3= 6 cuts minimum ...

5)27= 3*3*3 to form a larger cube which is completly cover so we required 5*5*5 cube ... so we require 125 cube and for addition cube it will be 125-27= 98