Statement 1 `a+b+c=18(a,b,cgt0)`, then the maximum value of abc is 216.
Statement 2 Maximum value occurs when `a=b=c`.

Options

A. Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1
B. Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1
C. Statement 1 is true, Statement 2 is false
D. Statement 1 is false, Statement 2 is true

Explanation

To solve the problem, we need to analyze the two statements provided and determine their validity using the Arithmetic Mean-Geometric Mean Inequality (AM-GM Inequality).

### Step-by-Step Solution:

1. **Understanding the Problem**: We are given that \( a + b + c = 18 \) where \( a, b, c > 0 \). We need to find the maximum value of the product \( abc \).

2. **Applying the AM-GM Inequality**: According to the AM-GM Inequality, for any non-negative real numbers \( a, b, c \):
\[ \frac{a + b + c}{3} \geq \sqrt[3]{abc} \]
This implies:
\[ \frac{18}{3} \geq \sqrt[3]{abc} \]
Simplifying this gives:
\[ 6 \geq \sqrt[3]{abc} \]

3. **Cubing Both Sides**: To eliminate the cube root, we cube both sides of the inequality:
\[ 6^3 \geq abc \]
Calculating \( 6^3 \):
\[ 6^3 = 216 \]
Therefore, we have:
\[ abc \leq 216 \]

4. **Finding When Equality Holds**: The equality in the AM-GM inequality holds when all the numbers are equal. Therefore, for \( a + b + c = 18 \) to achieve the maximum product \( abc \), we set:
\[ a = b = c \]
Let \( a = b = c = x \). Then:
\[ 3x = 18 \implies x = 6 \]
Thus, \( a = b = c = 6 \).

5. **Calculating the Maximum Product**: Now substituting back to find \( abc \):
\[ abc = 6 \times 6 \times 6 = 216 \]

6. **Conclusion**:
- Statement 1 is true: The maximum value of \( abc \) is indeed 216.
- Statement 2 is also true: The maximum value occurs when \( a = b = c = 6 \).

### Final Answer:
Both statements are true.