Multiple choice

Each of the questions given below consists of a statement and /or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. A cylindrical vessel contains 80% of water in it which is filled by a pipe. Find the total capacity of the cylindrical vessel. [Use π = 3] I. The difference between the curved surface area and the total surface area of the cylindrical vessel is 384 m2. II. The pipe took 72 minutes to fill the given quantity of water at the rate of 32 m3 per minute. III. The curved surface area and total surface area of the vessel is 720 m2 and 1104 m2 , respectively. IV. The cost of painting the curved surface area of the vessel at the rate of Rs. 5 per m2 is Rs. 3600.

  1. The data either in statement I alone or in statement IV alone are sufficient to answer the question

  2. The data either in statement I alone or in statement III alone are sufficient to answer the question.

  3. The data either in statement III alone or in statement IV alone are sufficient to answer the question.

  4. The data either in statement II alone or in statement III alone are sufficient to answer the question

  5. The data in any of the four statements I, II, III or IV alone are sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the capacity of a cylinder, we need its radius and height. Statement II provides the volume of water (32 * 72 = 2304 m^3) and the percentage filled (80%), allowing us to find the total capacity. Statement III provides the curved surface area and total surface area, which are sufficient to solve for radius and height, and thus the volume.

AI explanation

To find the total capacity, we need the vessel's full volume; statement II provides the volume of the 80% water directly by multiplying the pipe rate by the time, giving 32 * 72 = 2304 m^3, and dividing by 0.8 yields the total capacity. Statement III provides the curved surface area (2*pi*r*h = 720) and total surface area (2*pi*r*(r+h) = 1104), which allows solving for the radius and height to find the total volume. Statements I and IV only provide surface area relationships or costs, which give the curved surface area but lack the total surface area needed to find the radius and height independently. The data either in statement II alone or in statement III alone are sufficient to answer the question.

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