Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. Find both to find the relationship among them. Mark your answer accordingly. Quantity I: The area of the circle is 154 cm. The ratio of the radius of the Sphere and circle is 3:1. Find surface area of the sphere? Quantity II: The side of the square is equal to the breadth of the rectangle. The ratio of the length and breadth of the rectangle is 3 : 2. If the perimeter of the rectangle 70 cm, then find the sum of the area of the square and the area of the rectangle?

  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 beestablished
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A Correct answer
Explanation

Interpreting the circle's area as 154 cm^2 gives radius 7 cm, so the sphere radius is 21 cm and its surface area is 1764pi cm^2. For the rectangle, length and breadth are 21 cm and 14 cm, so the square plus rectangle area is 196 + 294 = 490 cm^2. Therefore, Quantity I is greater than Quantity II.

AI explanation

For Quantity I, using the circle area formula to find the radius gives r = sqrt(154*7/22) = 7 cm. The sphere radius is then 7 * 3 = 21 cm, and its surface area is 4*pi*21^2 = 5544 cm^2. For Quantity II, using the rectangle perimeter formula 2(L+W) = 70 gives length and breadth as 21 cm and 14 cm, making the square's side 14 cm; the combined area of the square and rectangle is 14^2 + 21*14 = 490 cm^2. Since 5544 cm^2 is greater than 490 cm^2, Quantity I > Quantity II.

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