Number of digits in the cube of a two digit number may be ____________

Answer

To determine the number of digits in the cube of a two-digit number, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Range of Two-Digit Numbers:**
- The smallest two-digit number is 10.
- The largest two-digit number is 99.

2. **Calculate the Cube of the Smallest Two-Digit Number:**
- Calculate \(10^3\):
\[ 10^3 = 1000 \]
- The number of digits in 1000 is 4.

3. **Calculate the Cube of the Largest Two-Digit Number:**
- Calculate \(99^3\):
\[ 99^3 = 99 \times 99 \times 99 \]
- First, calculate \(99 \times 99 = 9801\).
- Then, calculate \(9801 \times 99\):
\[ 9801 \times 99 = 970299 \]
- The number of digits in 970299 is 6.

4. **Determine the Range of Digits:**
- From the calculations:
- The cube of the smallest two-digit number (10) has 4 digits.
- The cube of the largest two-digit number (99) has 6 digits.
- Therefore, the number of digits in the cube of a two-digit number can be 4, 5, or 6.

### Conclusion:
The number of digits in the cube of a two-digit number may be **4, 5, or 6**.