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      Question

      The volumes of two hemispheres are in the ratio 1000:3375.

      Determine the ratio of their total surface areas. (Take π = 22/7)
      A 5:9 Correct Answer Incorrect Answer
      B 5:7 Correct Answer Incorrect Answer
      C 4:9 Correct Answer Incorrect Answer
      D 3:7 Correct Answer Incorrect Answer

      Solution

      ATQ,

      Volume of a hemisphere = (2/3) × π × radius³

      Let the radii of the two hemispheres be ‘A’ and ‘a’ unit’s respectively.

      So,

      [(2/3) × π × A³] : [(2/3) × π × a³] = 1000 : 3375

      ⇒ A³ : a³ = 1000 : 3375

      ⇒ A : a = 10 : 15 = 2 : 3

      Total surface area of a hemisphere = 3 × π × radius²

      So, required ratio = (3 × π × A²) : (3 × π × a²)

      ⇒ A² : a² = 2² : 3² = 4 : 9

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