Multiple choice

Passage

The following questions are accompanied by two statements A and B. You have to determine which statements(s) is/are sufficient/necessary to answer the questions.

Find the volume of right angle cone ? (A) Curved surface area of cone 18π units and T.S.A. of cone 50% more than curved surface area. (B) Volume of cylinder of twice the radius as that of cone & √3 time the height as that cone is 324π cubic units.

  1. Statement A alone is sufficient to answer the question, but statement B alone is not sufficient to answer the questions.

  2. Statement B alone is sufficient to answer the question, but statement A alone is not sufficient to answer the question.

  3. Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question.

  4. Either statement A or statement B by itself is sufficient to answer the question.

  5. Statements A and B taken together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement A gives CSA = 18pi and TSA = 1.5 * CSA = 27pi. Since TSA = CSA + pi*r^2, pi*r^2 = 9pi, r = 3. Using CSA = pi*r*l = 18pi, 3l = 18, l = 6. Height h = sqrt(l^2 - r^2) = sqrt(27) = 3*sqrt(3). Volume can be found. Statement B gives volume of a cylinder with double radius and sqrt(3) height, which allows finding the cone's dimensions. Both are sufficient.

AI explanation

Statement A provides the curved surface area as 18 pi and the total surface area as 27 pi, allowing you to find the base radius and then the slant height to calculate the cone's volume. Statement B gives the cylinder's volume as 324 pi with twice the cone's radius and square root of 3 times the cone's height, letting you solve for the cone's radius and height to find its volume. Since each statement independently provides enough variables to solve for the cone's dimensions, either statement alone is sufficient. Either statement A or statement B by itself is sufficient to answer the question.

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