Question 1198562
**1. Find the Radii**

* Radius of the larger base (R) = 18 inches / 2 = 9 inches
* Radius of the smaller base (r) = 14 inches / 2 = 7 inches

**2. Find the Height of the Frustum**

* Let 'h' be the height of the frustum.
* We have a right triangle formed by:
    * Slant height (l) = 25 inches
    * Height (h)
    * Difference in radii (R - r) = 9 - 7 = 2 inches

* Using the Pythagorean Theorem:
    * h² = l² - (R - r)²
    * h² = 25² - 2²
    * h² = 625 - 4
    * h² = 621
    * h = √621 inches

**3. Calculate the Volume of the Frustum**

* Volume (V) = (1/3) * π * h * (R² + Rr + r²) 
* V = (1/3) * π * √621 * (9² + 9*7 + 7²)
* V = (1/3) * π * √621 * (81 + 63 + 49)
* V = (1/3) * π * √621 * 193

**4. Express the Volume in the Given Form**

* V = (193/3) * π * √621 
* V = Χπ√γ 

* **Χ = 193/3** 
* **γ = 621**

**5. Find the Smallest Sum of Χ and γ**

* Sum = Χ + γ = (193/3) + 621 
* Sum = 193/3 + 1863/3 
* Sum = 2056/3 

**Therefore, the smallest sum of Χ and γ is 2056/3.**