Multiple choice

The following questions are accompanied by two statements (I) and (II). You have to determine which statements(s) is/are sufficient/necessary to answer the questions. (a) Statement (I) alone is sufficient to answer the question but statement (II) alone is not sufficient to answer the questions. (b) Statement (II) alone is sufficient to answer the question but statement (I) alone is not sufficient to answer the question. (c) Both the statements taken together are necessary to answer the questions, but neither of the statements alone is sufficient to answer the question. (d) Either statement (I) or statement (II) by itself is sufficient to answer the question. (e) Statements (I) and (II) taken together are not sufficient to answer the question. What is the volume of the sphere? I. Surface area of hemisphere is equal to the total surface area of the cylinder having radius and height in ratio 3 : 4. II. When we cut sphere into two hemi-sphere then total surface area is equal to the area of a circle whose radius is 21 cm.

  1. A

  2. B

  3. C

  4. D

  5. E
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement II provides the radius of the sphere (since surface area of a sphere is 4*pi*r^2 and two hemispheres have total surface area 3*pi*r^2 = area of circle with radius 21, which is pi*21^2). This allows calculation of the volume. Statement I involves a cylinder with unknown dimensions, so it is insufficient.

AI explanation

Statement two alone provides the total surface area of the two hemispheres, which is 3 times pi times r squared, and equates it to the area of a circle with radius 21 cm, meaning 3 times pi times r squared equals pi times 21 squared. This lets us solve directly for the radius of the sphere as 12.12 cm, which can then be put into the volume formula four thirds times pi times r cubed. Statement one only provides proportional information without any concrete measurements, making it insufficient. The result is B.

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