Question 1198556
Certainly, let's solve this problem.

**1. Find the Volume of the Cone**

* Volume of cone = (1/3) * π * r² * h 
    * Where:
        * r = radius of the base (5 cm)
        * h = height of the cone (12 cm)

* Volume of cone = (1/3) * π * (5 cm)² * 12 cm
* Volume of cone = 100π cm³

**2. Find the Volume of the Cylindrical Hole**

* Volume of cylinder = π * r² * h 
    * Where:
        * r = radius of the hole (5 cm / 2 = 2.5 cm)
        * h = height of the hole (12 cm)

* Volume of cylinder = π * (2.5 cm)² * 12 cm
* Volume of cylinder = 75π cm³

**3. Find the Volume of the Remaining Wood**

* Volume of remaining wood = Volume of cone - Volume of cylinder
* Volume of remaining wood = 100π cm³ - 75π cm³
* Volume of remaining wood = 25π cm³

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

* V = Χπ/γ cm³ 

* Comparing:
    * V = 25π cm³ 
    * V = Χπ/γ cm³

* We can see that:
    * Χ = 25 * γ 

* Since γ is a prime number, the smallest possible value for γ is 11 (the next prime number after 7 is 11).

* Therefore:
    * Χ = 25 * 11 = 275

**5. Calculate ∛Χ + γ**

* ∛Χ + γ = ∛275 + 11 
* ∛Χ + γ ≈ 6.47 + 11 
* ∛Χ + γ ≈ 17.47

**Therefore, ∛Χ + γ is approximately 17.47.**