Multiple choice

What is the area of the remaining portion of a circle of radius 14 cm when a square with the maximum possible area inscribed in it is removed from it? (Use ? = 22/7)

  1. 518 cm2

  2. 520 cm2

  3. 616 cm2

  4. 224 cm2
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D Correct answer
Explanation

Radius = 14. Area of circle = (22/7)*14*14 = 616. The largest inscribed square has a diagonal equal to the diameter (28). Side of square s: s*sqrt(2) = 28, so s = 28/sqrt(2) = 14*sqrt(2). Area of square = s^2 = 196*2 = 392. Remaining area = 616 - 392 = 224.

AI explanation

The area of the circle is found using the formula pi times the radius squared, so 22/7 times 14 times 14 equals 616 square centimeters. For the largest inscribed square, the diagonal equals the diameter of the circle, which is 28 centimeters, making the square's area half of the diagonal squared (1/2 times 28 times 28), or 392 square centimeters. Subtracting the area of the square from the circle's area leaves 616 minus 392, which equals 224 square centimeters.

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