In geometry a **cube** is a three dimension solid having **6** square faces, **12** edges and **8** corners.

In cube for any cut we will get one more piece. Example :for 1 cut, we get 2 pieces ,for 2 cut ,we get 3 pieces.

```
Example: If 15 cuts are to be made on a cube, then what is the maximum possible number of identical pieces that can be formed ?
```

A) 204

B) 125

C) 216

D) None of these

**Answer:**C) 216

**Explanation:**
Here 5 cuts in each axis (X,Y ,Z ).So we get 6 pieces in each axis. Then total 6*6*6=216

```
Example:What is the minimum possible number of cuts required to form 729 identical pieces from cube ?
```

A) 24

B) 21

C) 27

D) None of these

**Answer:**A) 24

**Explanation:**

9*9*9=729.So in each axis we get 9 pieces and for this 8 cuts required in each axis. So possible number of cuts required 8+8+8=24

```
Example:What is the least number of cuts required to form exactly 100 identical pieces from a cube ?
```

A) 13

B) 14

C) 11

D) None of these

**Answer:**C) 11

**Explanation:**

100 lies between 4*4*4=64 and 5*5*5=125.So for 100 pieces we take 4*5*5=100.So total cuts required 3+4+4=11