Multiple choice

Find the value of Q1 and Q2 and state the correct relationship.\newline\newlineQuantity I: Area of rectangle whose sides are in the ratio 20 : 9 and perimeter is 116 cm.\newlineQuantity II: Curved surface area of a cylinder of radius 14 cm and height equal to the side of square of area 64 cm$^2$.

  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
A Correct answer
Explanation

Quantity I: Rectangle sides in ratio 20:9, perimeter = 116 cm. Let sides be 20x and 9x. Perimeter = 2(20x + 9x) = 58x = 116, so x = 2. Area = 20x × 9x = 180x² = 180 × 4 = 720 cm². Quantity II: Cylinder radius = 14 cm. Height = side of square with area 64 cm², so side = 8 cm. Curved surface area = 2πrh = 2 × π × 14 × 8 = 224π ≈ 704 cm². Since 720 > 704, Quantity I > Quantity II. However, the claimed answer is A which states 'Quantity I > Quantity II', so agrees = true.

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