A right circular cylinder of radius r cm and height h cm ( where , h gt 2r) just encloses a sphere of diameter

Options

A. r cm
B. 2rcm
C. h cm
D. 2hcm

Explanation

To solve the problem, we need to determine the diameter of a sphere that is just enclosed by a right circular cylinder of radius \( r \) cm and height \( h \) cm, given that \( h > 2r \).

### Step-by-Step Solution:

1. **Understanding the Cylinder and Sphere Configuration**:
- A right circular cylinder has a radius \( r \) and height \( h \).
- The sphere is inscribed within the cylinder, meaning it touches the sides of the cylinder and the top and bottom faces.

2. **Identifying the Diameter of the Sphere**:
- The diameter of the sphere is equal to the distance across the sphere through its center.
- Since the sphere is inscribed in the cylinder, its diameter will be equal to the diameter of the circular base of the cylinder.

3. **Calculating the Diameter**:
- The radius of the cylinder is \( r \).
- Therefore, the diameter \( D \) of the sphere can be calculated as:
\[ D = 2 \times r \]

4. **Conclusion**:
- The diameter of the sphere that is just enclosed by the cylinder is \( 2r \) cm.

### Final Answer:
The diameter of the sphere is \( 2r \) cm.