Prove that the semi-vertical angle of the right circular cone of given volume and least curved surface is `cot^(-1)(sqrt(2))dot`

Explanation

To prove that the semi-vertical angle of the right circular cone of given volume and least curved surface area is \( \cot^{-1}(\sqrt{2}) \), we will follow these steps:

### Step 1: Define the Variables
Let:
- \( r \) = radius of the base of the cone
- \( h \) = height of the cone
- \( V \) = volume of the cone (constant)
- \( A \) = curved surface area of the cone
...