Show that the height of the cone of maximum volume that can be inscribed in a sphere of radius 12cm is 16cm.

Explanation

To solve the problem of finding the height of the cone of maximum volume that can be inscribed in a sphere of radius 12 cm, we will follow these steps:

### Step-by-Step Solution

1. **Understanding the Geometry**:
- We have a sphere with a radius \( R = 12 \) cm.
- We need to inscribe a cone within this sphere. Let the height of the cone be \( h \) and the radius of the base of the cone be \( r \).

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