Multiple choice

Directions: In the following question, we have two quantities given. Compare these quantities and answer accordingly with the following given options. Quantity I: The area of the circle inscribed in a square of side 28 cm. Quantity II: The area of the circle circumscribing a rectangle of length and breadth equal to 21 cm and 20 cm, respectively.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: Circle inscribed in square of side 28. Radius = 14. Area = pi * 14^2 = 196 * pi. Quantity II: Circle circumscribing rectangle 21x20. Diameter = sqrt(21^2 + 20^2) = sqrt(441 + 400) = sqrt(841) = 29. Radius = 14.5. Area = pi * 14.5^2 = 210.25 * pi. Quantity II > Quantity I.

AI explanation

For Quantity I, the radius of the circle inscribed in a square with side 28 cm is 14 cm, so its area is pi * 14^2 = 196pi. For Quantity II, the radius of the circle circumscribing a 21 cm by 20 cm rectangle is half of its diagonal; using the Pythagorean theorem, the diagonal is sqrt(21^2 + 20^2) = sqrt(441 + 400) = sqrt(841) = 29 cm, making the area pi * (14.5)^2 = 210.25pi. Comparing the two calculated areas, 196pi is less than 210.25pi, so Quantity I < Quantity II.

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