Multiple choice

A circle is inscribed in a square of side length $6$. The area of the region inside the square but outside the circle is

  1. $36\pi$
  2. $26\pi - 9$
  3. $26\pi - 36$
  4. $36 - 9\pi$
  5. $9\pi - 36$
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D Correct answer
Explanation

The area of the square is 6^2 = 36. The inscribed circle has a diameter of 6, so its radius is 3, and its area is pi * 3^2 = 9pi. The region inside the square but outside the circle is 36 - 9pi.

AI explanation

The diameter of the inscribed circle equals the side length of the square, making the radius 3. The area of the square is 6 squared, which is 36, and the area of the circle is pi times 3 squared, which is 9 times pi. Subtracting the circle's area from the square's area gives the area of the outside region, yielding 36 minus 9 times pi.

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