Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is `8/(27)`of the volume of the sphere.

Explanation

To prove that the volume of the largest cone that can be inscribed in a sphere of radius \( R \) is \( \frac{8}{27} \) of the volume of the sphere, we will follow these steps:

### Step 1: Define the volumes
The volume \( V_S \) of the sphere with radius \( R \) is given by:
\[ V_S = \frac{4}{3} \pi R^3 \]
The volume \( V_C \) of the cone with height \( h \) and radius \( x \) is given by:
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