To solve the problem (assuming it refers to the ratio of the area of the circumscribed circle around a square to the inscribed circle inside the square), follow these steps:

Step 1: Define the square's side length

Let the side length of the square be (s).

Step 2: Calculate the inscribed circle's area

The inscribed circle’s diameter equals the square’s side length.

• Radius (r_1 = \frac{s}{2})
• Area (A_1 = \pi r_1^2 = \pi \left(\frac{s}{2}\right)^2 = \frac{\pi s^2}{4})

Step 3: Calculate the circumscribed circle's area

The circumscribed circle’s diameter equals the square’s diagonal ((s\sqrt{2})).

• Radius (r_2 = \frac{s\sqrt{2}}{2} = \frac{s}{\sqrt{2}})
• Area (A_2 = \pi r_2^2 = \pi \left(\frac{s}{\sqrt{2}}\right)^2 = \frac{\pi s^2}{2})

Step 4: Find the ratio

Ratio of the circumscribed circle area to the inscribed circle area:
(\frac{A_2}{A_1} = \frac{\frac{\pi s^2}{2}}{\frac{\pi s^2}{4}} = 2)

Answer: (\boxed{2})

作者声明:本文包含人工智能生成内容。