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      Question

      The combined height and radius of a right circular cone

      total 31 cm, with the height exceeding the radius by 17 cm. Calculate the curved surface area of the cone.
      A 450 sq cm Correct Answer Incorrect Answer
      B 550 sq cm Correct Answer Incorrect Answer
      C 650 sq cm Correct Answer Incorrect Answer
      D 510 sq cm Correct Answer Incorrect Answer
      E 490 sq cm Correct Answer Incorrect Answer

      Solution

      Let the radius and height of the cone be 'r' cm and 'h' cm respectively. We have, (r + h) = 31 And h = r + 17 So, r + h = r + r + 17 = 31 Or, r = (31 - 17) ÷ 2 = 7 cm So, h = 7 + 17 = 24 cm Also, slant height of the cone =  √(r2 + h2)  =  √(7 2 + 24 2)  = 25 cm Therefore, curved surface area of the cone = π X radius X slant height = (22/7) X 7 X 25 = 550 cm2

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