Write True or False and justify your answer in each of the following:
The volume of the largest right circular cone that can be fitted in a cube whose edge is `2r` equals to the volume of a hemisphere radius `r`.

Explanation

To determine whether the statement is true or false, we need to compare the volume of the largest right circular cone that can fit inside a cube with an edge of \(2r\) to the volume of a hemisphere with radius \(r\).

### Step-by-Step Solution:

1. **Identify the dimensions of the cube and cone**:
- The edge of the cube is given as \(2r\).
- The diameter of the base of the cone will be equal to the side of the cube, which is \(2r\).
- Therefore, the radius \(R\) of the base of the cone is:
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