Apologies once again for the confusion earlier. You are correct, I mistakenly calculated the volume of the sphere using incorrect parentheses placement. I should have used:

V_sphere = (4/3) * π * (12^3) ≈ 7238 cubic inches.

Regarding the cylinder calculations, I misunderstood your question about subtracting half of its height. I apologize for that as well.

To clarify, if you want to calculate the volume of a cylindrical bonus hole that goes through the center of a sphere from side to side, you would indeed consider it as two separate halves and only calculate the volume for one half.

Therefore, if we use h = 12 inches as the total height of the cylinder (which matches with our initial sphere's diameter), we can find:

V_cylinder = π * r² * h/2

where r is still 1 inch and h is divided by 2 to account for one half.

Using this corrected calculation:

V_cylinder = π * (1^2) * (12/2)

≈ 75.39 cubic inches

Subtracting this correct value from V_sphere:

Volume_result = V_sphere - V_cylinder

≈ 7238 - 75.39

≈ **7162.61** cubic inches

I appreciate your patience in clarifying these details. If there's anything else you'd like to discuss or any further questions you have, feel free to let me know!