Two solid hemispheres of the same base radius \(r\) are joined along their bases. The curved surface area of the new solid is
\(4\pi r^2\)
\(6\pi r^2\)
\(3\pi r^2\)
\(8\pi r^2\)
Step 1: Recall that a hemisphere is half of a sphere.
Step 2: Each hemisphere has a curved surface area (CSA) given by:
\( \text{CSA of one hemisphere} = 2\pi r^2 \).
Step 3: When two hemispheres of radius \(r\) are joined together along their flat bases, the flat parts disappear, and they form a complete sphere.
Step 4: The surface area of a sphere is entirely curved surface (no flat faces).
Formula: \( \text{CSA of a sphere} = 4\pi r^2 \).
Step 5: Therefore, the new solid (a sphere) has curved surface area:
\( 4\pi r^2 \).
Final Answer: Option A (\(4\pi r^2\)).