## Cubes

#### Cubes

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

1. For minimum number of cuts we will get 50 from 2 x 5 x 5 and cuts is 1 + 4 + 4 = 9

##### Correct Option: C

For minimum number of cuts we will get 50 from 2 x 5 x 5 and cuts is 1 + 4 + 4 = 9

Direction: 216 cubes of similar size are arranged in the form of the bigger cube (6 cubes on each side, i.e.., 6 x 6 x 6) all the exposed surfaces are painted.

1. How many of the cubes have 0 faces painted?

1. Since total number of cubes is hence in the formula we will substitute n = 6
Number of the cubes with 0 faces painted is (6 - 2)3 = 43 = 64

##### Correct Option: A

Since total number of cubes is hence in the formula we will substitute n = 6
Number of the cubes with 0 faces painted is (6 - 2)3 = 43 = 64

1. How many of the cubes have 2 most faces painted?

1. Since total number of cubes is hence in the formula we will substitute n = 6
Number of the cubes with 2 faces painted is 6(6 - 2)2
= 6 x 16 = 96

##### Correct Option: C

Since total number of cubes is hence in the formula we will substitute n = 6
Number of the cubes with 2 faces painted is 6(6 - 2)2
= 6 x 16 = 96

1. How many of the cubes have at most faces painted?

1. Since total number of cubes is hence in the formula we will substitute n = 6
At most 2 faces painted means number of cubes with 0 face painted + number of cubes with 1 face painted + number of cubes
with 2 face painted = 64 + 48 + 96 = 208

##### Correct Option: A

Since total number of cubes is hence in the formula we will substitute n = 6
At most 2 faces painted means number of cubes with 0 face painted + number of cubes with 1 face painted + number of cubes with 2 face painted = 64 + 48 + 96 = 208

1. How many of the cubes have at least 2 faces painted?

1. Since total number of cubes is hence in the formula we will substitute n = 6
At least 2 faces painted means number of cubes with 2 face painted + number of cubes with 3 face painted = 96 + 8 = 104.

##### Correct Option: B

Since total number of cubes is hence in the formula we will substitute n = 6
At least 2 faces painted means number of cubes with 2 face painted + number of cubes with 3 face painted = 96 + 8 = 104.