Sania wanted to cut a cubical cake into 120 identical pieces applying minimum number of 'n' cuts. Later on she realised that she had to cut this cake into maximum number of identical pieces i.e., 125 pieces. Now she applies the number of cuts is:

Options

A. n
B. n+5
C. n+1
D. can't be determined

Answer

To determine how many cuts Sania needs to make to cut a cubical cake into 125 identical pieces, we can follow these steps:

### Step 1: Understand the relationship between cuts and pieces.
When cutting a cube into identical pieces, the number of pieces \( P \) created by \( n \) cuts can be calculated using the formula:
\[ P = (n + 1)^3 \]
This formula arises because each cut increases the number of sections along that dimension by one.

### Step 2: Calculate the number of cuts for 120 pieces.
First, we need to find \( n \) such that:
\[ (n + 1)^3 = 120 \]
Taking the cube root of both sides:
\[ n + 1 = \sqrt[3]{120} \]
Calculating the cube root:
\[ \sqrt[3]{120} \approx 4.93 \]
Thus, we can approximate \( n + 1 \) to the nearest whole number, which is 5. Therefore:
\[ n + 1 = 5 \implies n = 4 \]

### Step 3: Calculate the number of cuts for 125 pieces.
Now, we need to find how many cuts are needed to create 125 pieces:
\[ (n + 1)^3 = 125 \]
Taking the cube root:
\[ n + 1 = \sqrt[3]{125} \]
Calculating the cube root:
\[ \sqrt[3]{125} = 5 \]
Thus:
\[ n + 1 = 5 \implies n = 4 \]

### Conclusion:
Sania will still need to make \( n = 4 \) cuts to cut the cake into 125 identical pieces.

### Final Answer:
The number of cuts required to cut the cake into 125 pieces is \( n = 4 \).