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Find the volume of the cylinder. (I) The curved surface area of the cylinder is 1760 cm², and the total surface area of the cylinder is 70% more than its curved surface area. (II) The volume of the cylinder is twice that of a cone. The radius of the cylinder and cone is equal, and the ratio of the height of the cylinder to that of the cone is 2:3. The height of the cone is 30 cm.

1. Statement (I) alone is sufficient to answer the question but statement (II) alone is not sufficient to answer the question.
2. Statement (II) alone is sufficient to answer the question but statement (I) alone is not sufficient to answer the question.
3. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.
4. Either statement (I) or statement (II) by itself is sufficient to answer the question.

Correct answer: Statement (I) alone is sufficient to answer the question but statement (II) alone is not sufficient to answer the question.

Solution

Statement (I) gives curved surface area and total surface area, which are enough to determine the radius and height of the cylinder uniquely. Statement (II) does not provide enough independent information to fix the cylinder's volume on its own.

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