## Cubes

#### Cubes

1. If total number of cuts is 10 then find the minimum number of pieces that can be obtained.

1. If total number of cuts is 10 then minimum number of pieces is 11 when cut is made in one plane only.

##### Correct Option: B

If total number of cuts is 10 then minimum number of pieces is 11 when cut is made in one plane only.

1. If total number of cuts is 10 then find the maximum number of pieces that can be obtained.

1. If total number of cut is 10 then for maximum number of pieces these cuts have to be well distributed in three planes. For 10 cuts,
3,3 and 4 is the distribution of cuts.

##### Correct Option: A

If total number of cut is 10 then for maximum number of pieces these cuts have to be well distributed in three planes. For 10 cuts, 3,3 and 4 is the distribution of cuts.
Hence total number of pieces is
(3 + 3)(3 + 1)(4 + 1) = 4 x 4 5 = 80

1. If total number of cuts is 20 then find the ratio of maximum and minimum of pieces that can be obtained.

1. For maximum number of pieces cuts has to be 6, 7 and 7 and maximum number of pieces is (6 + 1)(7 + 1)(7 + 1) = 7 x 8 x 8 = 448.
Minimum number of pieces is 20 + 1 = 21.

##### Correct Option: B

For maximum number of pieces cuts has to be 6, 7 and 7 and maximum number of pieces is (6 + 1)(7 + 1)(7 + 1) = 7 x 8 x 8 = 448.
Minimum number of pieces is 20 + 1 = 21.
Hence required ratio is 448:21

1. If total number of pieces (Smaller cubes/cuboids) is 45 then find the possible number of cuts.

1. If 45 = 1 x 1 x 45 then we require only 44 cuts in one plane.
If 1 x 3 x 15 then we require 2 cuts in one plane and 14 cuts in other plane so total number of cuts is 2 + 14 = 16.
If 1 x 5 x 9 the we require 4 cuts in one plane and 8 cuts in other plane so total number of cuts is 4 + 8 = 12
If 3 x 3 x 5 then we require 2 cuts in one plane, 2 cuts in 2nd plane and 4 cuts in 3rd plane so total number of cuts is 2 + 2 + 4 = 8.

##### Correct Option: B

If 45 = 1 x 1 x 45 then we require only 44 cuts in one plane.
If 1 x 3 x 15 then we require 2 cuts in one plane and 14 cuts in other plane so total number of cuts is 2 + 14 = 16.
If 1 x 5 x 9 the we require 4 cuts in one plane and 8 cuts in other plane so total number of cuts is 4 + 8 = 12
If 3 x 3 x 5 then we require 2 cuts in one plane, 2 cuts in 2nd plane and 4 cuts in 3rd plane so total number of cuts is 2 + 2 + 4 = 8.

1. Find the maximum number of cuts required to get 50 pieces.

1. For maximum number of cuts it has to be in one cut only, so number of cuts is 49

##### Correct Option: A

For maximum number of cuts it has to be in one cut only, so number of cuts is 49