Multiple choice

In the following questions, two quantities are given as Quantity I and Quantity II. Find the correct relationship. $The perimeter of a square is equal to twice the perimeter of a rectangle of length 11 cm & breadth 10 cm \text{ Quantity I: } Find the circumference of a semicircle whose diameter is equal to the side of the square. \text{ Quantity II: } Find the circumference of another semicircle whose radius is 14 cm$

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rectangle perimeter = 2(11+10) = 42 cm. Square perimeter = 2 × 42 = 84 cm, so side = 21 cm. Quantity I: Semicircle with diameter 21 cm has radius 10.5 cm. Circumference of semicircle = πr + 2r = (π × 10.5) + 21 ≈ 33 + 21 = 54 cm. Quantity II: Semicircle with radius 14 cm has circumference = πr + 2r = (π × 14) + 28 ≈ 44 + 28 = 72 cm. Clearly 72 > 54, so Quantity II exceeds Quantity I.

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