Let the area of the largest possible square inscribed in a circle of unit radius be x. Let the area of the largest possible circle inscribed in a square of unit side length be y. What is the relation between x and y?

  1. A. \pi x = 2y
  2. B. 2\pi x = y
  3. C. \pi x = 4y
  4. D. \pi x = 8y ✓

Correct Answer: D. \pi x = 8y

Explanation

For a square inscribed in a circle of radius 1, its diagonal is 2, so its area x = \frac{2^2}{2} = 2. For a circle inscribed in a square of side 1, its radius is \frac{1}{2}, so its area y = \pi \times (\frac{1}{2})^2 = \frac{\pi}{4}. Thus, \pi x = 2\pi and 8y = 8(\frac{\pi}{4}) = 2\pi, meaning \pi x = 8y.

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