Multiple choice

What is the ratio of the area of a square that circumscribes a circle to the area of a square that inscribes the same circle?

  1. 4

  2. 3

  3. 2

  4. 1
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A square circumscribing a circle of radius r has a side length of 2r, so its area is 4r^2. A square inscribing a circle of radius r has a diagonal of 2r, so its side length is r*sqrt(2) and its area is 2r^2. The ratio of the areas is 4r^2 / 2r^2 = 2.

AI explanation

Let the radius of the circle be r, so the diameter is 2r. The inscribed square has a diagonal equal to the circle's diameter of 2r, which gives it an area of (2r)^2 / 2 = 2r^2. The circumscribed square has a side length equal to the circle's diameter of 2r, making its area (2r)^2 = 4r^2. Therefore, the ratio of the area of the circumscribed square to the inscribed square is 4r^2 / 2r^2 = 2.

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