Multiple choice

The area of the square that can be inscribed in a circle of radius $12 cm$ is

  1. $72 cm^{2}$
  2. $144 cm^{2}$
  3. $288 cm^{2}$
  4. $576 cm^{2}$
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C Correct answer
Explanation

A square inscribed in a circle has a diagonal equal to the circle's diameter. Diameter = 2 * 12 = 24 cm. Let side of square be s. s^2 + s^2 = 24^2 => 2s^2 = 576 => s^2 = 288. Area of square = s^2 = 288 cm^2.

AI explanation

When a square is inscribed in a circle, its diagonal is equal to the diameter of the circle. With a circle radius of 12 centimeters, the diameter is 24 centimeters, which is the diagonal of the square. The area of a square can be calculated as half the square of its diagonal, so the area is half of 24 squared. Half of 576 is 288, so the area of the inscribed square is 288 square centimeters.

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