Multiple choice

Find the value of quantities and state the correct relationship. ( \text{A hemisphere of radius 4 cm is to be shipped in a shipping box of rectangular shape. The dimension of the box are consecutive odd numbers.} ) ( \text{Quantity I: Minimum volume of box required to have the shipment possible.} ) ( \text{Quantity II: 960 cm}^3 )

  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
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A Correct answer
Explanation

Quantity I: The hemisphere radius is 4 cm, so its minimum bounding box must have dimensions at least 8 cm x 8 cm x 4 cm (diameter x diameter x height). With consecutive odd dimensions, the smallest such box is 7 x 9 x 11 or 9 x 11 x 13. Testing 9x11x13: volume = 1287 cm³, which is > 960 cm³. Therefore Quantity I > Quantity II.

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