Multiple choice

A square is drawn such that its vertices are lying on a circle of radius 201 mm. What is the ratio of area of circle to that of square?

  1. 11 : 7

  2. 7 : 11

  3. 20 : 19

  4. 19 : 20
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A Correct answer
Explanation

Radius R = 201. Square diagonal = 2R = 402. Side of square s = 402 / sqrt(2) = 201 * sqrt(2). Area of circle = pi * R^2 = pi * 201^2. Area of square = s^2 = 2 * 201^2. Ratio = (pi * 201^2) / (2 * 201^2) = pi / 2. Using pi = 22/7, ratio = (22/7) / 2 = 11/7.

AI explanation

When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. If the circle has a radius of 201 mm, its diameter is 402 mm. Using the Pythagorean theorem, the side of the square is s = 402 / sqrt(2), making the area of the square s^2 = (402^2) / 2 = 80802 square mm. The area of the circle is pi * r^2, which is (22/7) * 201 * 201 = 127311 square mm. The ratio of the area of the circle to that of the square is 127311 divided by 80802, which simplifies to approximately 1.575, or 11 : 7.

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