If two solid hemispheres of same base radius r are joined together along their bases, them curved surface area of the this new solid is

Options

A. `4pir^(2)`
B. `6pir^(2)`
C. `3pir^(2)`
D. `8pir^(2)`

Explanation

To find the curved surface area of the solid formed by joining two solid hemispheres along their bases, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Shape**: When two hemispheres are joined together along their bases, they form a complete sphere.

2. **Formula for Curved Surface Area of a Sphere**: The formula for the curved surface area (C.S.A) of a sphere is given by:
\[ \text{C.S.A of sphere} = 4\pi r^2 \]
where \( r \) is the radius of the sphere.

3. **Applying the Formula**: Since the two hemispheres have the same base radius \( r \), we can directly use the radius \( r \) in the formula for the curved surface area of the sphere:
\[ \text{C.S.A} = 4\pi r^2 \]

4. **Conclusion**: Therefore, the curved surface area of the new solid formed by joining the two hemispheres is:
\[ \text{Curved Surface Area} = 4\pi r^2 \]

### Final Answer:
The curved surface area of the solid formed by joining two solid hemispheres of radius \( r \) is \( 4\pi r^2 \).

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