Multiple choice

The area of the square that can be inscribed in a circle of radius $8$ cm is :

  1. $256$ $cm^2$
  2. $128$ $cm^2$
  3. $64 \sqrt{2} cm^2$
  4. $64$ $cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A square inscribed in a circle has a diagonal equal to the circle's diameter. Diameter = 2 * 8 = 16 cm. Let side be s. s^2 + s^2 = 16^2 = 256. 2s^2 = 256, s^2 = 128. The area of the square is s^2 = 128 cm^2.

AI explanation

For a square inscribed in a circle, the diagonal of the square equals the diameter of the circle, which is 2 times 8, or 16 cm. Using the relation between a square's side (s) and diagonal (d), d = s times the square root of 2, so the side is 16 divided by the square root of 2, which simplifies to 8 times the square root of 2 cm. The area is the side squared, yielding 128 square cm.

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