6: 108 :: 10: ?

Options

A. 125
B. 300
C. 500
D. 225

Explanation

To solve the analogy problem \(6 : 108 :: 10 : ?\), we need to find the value that corresponds to 10 in the same way that 108 corresponds to 6.

### Step-by-Step Solution:

1. **Understand the relationship in the first pair (6 and 108)**:
- We need to identify how 6 relates to 108. The video suggests that we can use the cube of the first number.
- Calculate the cube of 6:
\[ 6^3 = 216 \]
- Now, divide this result by 2:
\[ \frac{216}{2} = 108 \]
- So, the relationship can be expressed as:
\[ \text{If } x = 6, \text{ then } \frac{x^3}{2} = 108 \]

2. **Apply the same relationship to the second pair (10 and ?)**:
- Now, we need to find the value of the question mark when the first number is 10.
- Calculate the cube of 10:
\[ 10^3 = 1000 \]
- Divide this result by 2:
\[ \frac{1000}{2} = 500 \]
- Therefore, the value corresponding to 10 is:
\[ ? = 500 \]

3. **Conclusion**:
- The final answer is:
\[ 10 : 500 \]

### Final Answer:
The value of the question mark is \(500\).