Observe the pattern given below
`1^(3)=1`
`2^(3)=3+5`
`3^(3)=7+9+11`
`4^(3)=13+15+17+19`
According to this pattern, the number of consecutive odd numbers whose sum equals `9^(3)` is

Options

A. 3
B. 9
C. 12
D. 15

Answer

To solve the problem, we need to identify the pattern in the sums of consecutive odd numbers that equal the cubes of integers.

### Step-by-Step Solution:

1. **Identify the pattern**:
- We observe that:
- \(1^3 = 1\) (which is the first odd number)
- \(2^3 = 3 + 5\) (which are the next two odd numbers)
- \(3^3 = 7 + 9 + 11\) (which are the next three odd numbers)
- \(4^3 = 13 + 15 + 17 + 19\) (which are the next four odd numbers)

2. **Generalize the pattern**:
- From the observations, we can conclude that for \(n^3\), the sum consists of \(n\) consecutive odd numbers.
- Specifically, the sum of the first \(n\) odd numbers starting from the appropriate point.

3. **Determine the number of odd numbers for \(9^3\)**:
- We need to find the number of consecutive odd numbers that sum up to \(9^3\).
- According to the pattern, for \(n = 9\), we will need \(9\) consecutive odd numbers.

4. **Conclusion**:
- Therefore, the number of consecutive odd numbers whose sum equals \(9^3\) is \(9\).

### Final Answer:
The number of consecutive odd numbers whose sum equals \(9^3\) is **9**.