Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is `(4r)/3`.

Explanation

To find the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius \( r \), we will follow these steps:

### Step 1: Understanding the Geometry
Consider a right circular cone inscribed in a sphere of radius \( R \). The height of the cone is \( h \) and the radius of the base of the cone is \( r \). The relationship between the radius of the sphere, the height of the cone, and the radius of the cone can be expressed using the Pythagorean theorem:

\[ R^2 = r^2 + \left( R - h \right)^2 \]
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