Multiple choice

A square is inscribed within a circle of radius 10 centimeters. Use 3.14 for the value of π. Quantity A Area of the circle that is not covered by the square Quantity B 30 square centimeters

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the given data.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Circle area = pi * r^2 = 3.14 * 100 = 314. Square inscribed in circle has diagonal = 2r = 20. Side s = 20/sqrt(2) = 10*sqrt(2). Square area = s^2 = 200. Area not covered = 314 - 200 = 114. 114 > 30.

AI explanation

The circle area is pi times 10 squared, giving 314 square centimeters. The diagonal of the inscribed square is the diameter of 20 centimeters, so its area is half of 20 squared, which is 200 square centimeters. The uncovered area is 314 minus 200, equaling 114 square centimeters, which is greater than the 30 square centimeters in Quantity B.

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