Multiple choice

Following questions contain two statements as statement I and statement II. You have to determine which statement/s is/are necessary to answer the question and give answer as, What is the height of the cone? Statement I: The height of the cone is 17 cm more than that of the radius of the cone. Statement II: The volume of the cone is 1232 cm2 and the total surface area of the cone is 704 cm2 .

  1. 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

  2. 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

  3. The data either in statement I alone or in statement II alone is sufficient to answer the question

  4. The data given in both statements I and II together are not sufficient to answer the question

  5. The data given in both statements I and II together are necessary to answer the question.
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D Correct answer
AI explanation

To find the exact height of the cone, a concrete numerical value for either the height or the radius is required. Statement I only provides a relative difference between the height and the radius without giving any starting values. Statement II provides the volume and total surface area, but for a cone, these two equations involve three geometric variables including the radius, the height, and the slant height. The slant height is related to the radius and height by the Pythagorean theorem, meaning we have a system of two equations with three unknown variables, which is mathematically insufficient to solve for a unique height.

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