(Solved): If the infinite region \( \Omega=\left\{(x, y) \mid x \geq 1,0 \leq y \leq \frac{1}{x}\right\} \) ...

If the infinite region \( \Omega=\left\{(x, y) \mid x \geq 1,0 \leq y \leq \frac{1}{x}\right\} \) is rotated about the \( \boldsymbol{x} \)-axis, how about the volume of the resulting solid and its surface area? (A) Volume is finite. Surface area is finite. (B) Volume is infinite. Surface area is finite. (C) Volume is finite. Surface area is infinite. (D) Volume is infinite. Surface area is infinite.