The value of `(6.35 xx 6.35 xx 6.35 + 3.65 xx 3.65 xx 3.65)/(63.5 xx 63.5 + 36.5 xx 36.5-63.5 xx 36.5)` is equal to

Options

A. 0.01
B. 1000
C. 0.1
D. 1

Answer

To solve the problem step by step, we will use the formula for the sum of cubes and some algebraic manipulation.

### Step-by-Step Solution:

1. **Identify the Components**:
We have \( a = 6.35 \) and \( b = 3.65 \). We need to calculate \( a^3 + b^3 \) and \( a^2 + b^2 - ab \).

2. **Use the Sum of Cubes Formula**:
The formula for the sum of cubes is:
\[ a^3 + b^3 = (a + b)(a^2 - ab + b^2) \]
Thus, we can express \( a^3 + b^3 \) as:
\[ a^3 + b^3 = (6.35 + 3.65)(6.35^2 - 6.35 \cdot 3.65 + 3.65^2) \]

3. **Calculate \( a + b \)**:
\[ a + b = 6.35 + 3.65 = 10 \]

4. **Calculate \( a^2 \), \( b^2 \), and \( ab \)**:
\[ a^2 = (6.35)^2 = 40.3225 \]
\[ b^2 = (3.65)^2 = 13.3225 \]
\[ ab = 6.35 \cdot 3.65 = 23.2275 \]

5. **Calculate \( a^2 - ab + b^2 \)**:
\[ a^2 + b^2 - ab = 40.3225 + 13.3225 - 23.2275 = 30.4175 \]

6. **Calculate \( a^3 + b^3 \)**:
\[ a^3 + b^3 = 10 \cdot 30.4175 = 304.175 \]

7. **Calculate the Denominator**:
We need to compute \( 63.5^2 + 36.5^2 - 63.5 \cdot 36.5 \):
\[ 63.5^2 = 4032.25 \]
\[ 36.5^2 = 1332.25 \]
\[ 63.5 \cdot 36.5 = 2327.75 \]
\[ 63.5^2 + 36.5^2 - 63.5 \cdot 36.5 = 4032.25 + 1332.25 - 2327.75 = 3036.75 \]

8. **Final Calculation**:
Now we can substitute back into the original expression:
\[ \frac{a^3 + b^3}{63.5^2 + 36.5^2 - 63.5 \cdot 36.5} = \frac{304.175}{3036.75} \]

9. **Simplify the Fraction**:
\[ \frac{304.175}{3036.75} \approx 0.1 \]

### Conclusion:
The value of the expression is approximately \( 0.1 \).