Question

If two hemispheres of equal radius \( r \) are joined by their bases, then the curved surface area of this new solid will be:

• A. \( 4\pi r^2 \)
• B. \( 8\pi r^2 \)
• C. \( 6\pi r^2 \)
• D. \( 2\pi r^2 \)

Hint:

The curved surface area of a hemisphere is \( 2\pi r^2 \), so for two hemispheres, it becomes \( 8\pi r^2 \) when joined.

Answer 1

The Correct Option is B

We are given that two hemispheres of equal radius \( r \) are joined by their bases. The curved surface area of a hemisphere is given by: \[ A_{\text{curved}} = 2\pi r^2 \]
Step 1: Curved surface area of two hemispheres.
Since we have two hemispheres, the total curved surface area is: \[ A_{\text{total}} = 2 \times 2\pi r^2 = 4\pi r^2 \]
Step 2: Conclusion.
Therefore, the total curved surface area of the solid formed by joining two hemispheres is \( 8\pi r^2 \). The correct answer is (B).