Multiple choice

A square is inscribed in a circle. If the side of the square is 14 cm, what is the area (in sq. cm) of the circle?

  1. 49π

  2. 77π

  3. 121π

  4. 98π
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D Correct answer
Explanation

A square inscribed in a circle has its diagonal equal to the diameter of the circle. For a square with side 14 cm, the diagonal is 14 * sqrt(2) cm. The radius is half the diameter, so r = 7 * sqrt(2) cm. The area of the circle is pi * r^2 = pi * (7 * sqrt(2))^2 = pi * 49 * 2 = 98 * pi.

AI explanation

The diagonal of the inscribed square forms the diameter of the circle. Using the Pythagorean theorem, the diagonal is the square root of (14 squared plus 14 squared), or 14 times the square root of 2 cm. The radius is half the diameter, so the area of the circle is pi times the square of (7 times the square root of 2), which simplifies to 98pi.

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