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      Question

      A right circular cone is surmounted by a hemisphere. The

      base radius of the cone is equal to the radius of the hemisphere. The diameter of the hemisphere is 12 cm while the height of the cone is 8 cm. Find the cost of painting the compound object if it costs ₹50 to paint a cm².
      A ₹3,300 Correct Answer Incorrect Answer
      B ₹10,371 Correct Answer Incorrect Answer
      C ₹6,600 Correct Answer Incorrect Answer
      D ₹4,500 Correct Answer Incorrect Answer

      Solution

      Radius = 12 / 2 = 6 cm Since the right circular cone is surmounted on a hemisphere, the area of the base.   = 2 π ×62 = 72 π cm² Slant Height = √62 +√82 = 10 cm Hence, the total surface area of the cone is surmounted on the hemisphere. The curved surface area of the cone + the area of the base=π× 6 × 10 + 72π=132π Thus, the cost of painting the compound object = (50 × 132π) / π = 6600   The cost of painting the compound object is ₹6600.

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