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      Question

      What is the curved surface area of a right circular

      cylinder? I. The area of the base of the cylinder is 154 cm². II. The volume of the cylinder is 1540 cm³. Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer – 
      A If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      B If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question. Correct Answer Incorrect Answer
      C If the data either in statement I alone or in statement II alone is sufficient to answer the question. Correct Answer Incorrect Answer
      D If the data in both statements I and II together are necessary to answer the question. Correct Answer Incorrect Answer
      E If the data even in both statements I and II together are not sufficient to answer the question. Correct Answer Incorrect Answer

      Solution

      Curved surface area of the cylinder = 2πrh From I. Area of the base is 154 cm² ∴πr² = 154 = 22/7× r² = 154 r² = 7 × 7 r = 7 cm But we can’t find the height of the cylinder. Hence I alone is not sufficient. From II. Volume of the cylinder = πr²h = 1540 So, there are two variables r and h. Hence II alone is not sufficient. From I and II. Volume of the cylinder = πr²h. = 22/7× 7 × 7 × h = 1540 ∴ h = 10 cm ∴ Curved surface area of the cylinder = 2πrh = 2 ×22/7× 7 × 10 = 440 cm²  Thus, both the statements together are required to answer the question.

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