곡면 $S= \left \{\left (x, y, z \right) | 1 \leq x^2 + y^2 \leq 2, z=x^2 - y^2 \right.$ 의 넓이는?

• ①$\displaystyle \frac{\pi} {6} \left (24-5 \sqrt 5 \right)$
• ②$\displaystyle \frac{5 \pi} {6} \left (5- \sqrt 5 \right)$
• ③$\displaystyle \frac{\pi} {6} \left (26-5 \sqrt 5 \right)$
• ④$\displaystyle \frac{\pi} {6} \left (27-5 \sqrt 5 \right)$
• ⑤$\displaystyle \frac{\pi} {6} \left (28-5 \sqrt 5 \right)$