Multiple choice

The area of a square that can be inscribed in a circle of radius r is

  1. $ \displaystyle r^{2} $
  2. $ \displaystyle 2r^{2} $
  3. $ \displaystyle 4r^{2} $
  4. $ \displaystyle \pi r^{2} $
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B Correct answer
Explanation

A square inscribed in a circle has a diagonal equal to the circle's diameter (2r). Area of square = (diagonal^2) / 2 = (2r)^2 / 2 = 4r^2 / 2 = 2r^2.

AI explanation

For a square inscribed in a circle, the diagonal of the square equals the diameter of the circle, which is 2r. Using the relation between a square's area and its diagonal, the area is half the square of the diagonal. Therefore, the area is half of the square of 2r, which is 2r squared.

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