Multiple choice

Directions: The question given below is followed by two statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. What is the radius of the sphere? I. The cost of painting the surface area is Rs. 20 per m2. II. The sphere was formed by melting a cube of side 2 m.

  1. The question can be answered by using statement I alone, but cannot be answered by using statement II alone.

  2. The question can be answered by using statement II alone, but cannot be answered by using statement I alone.

  3. Both statements I and II together are required to answer the question.

  4. The answer can be found by using either of the two statements alone.

  5. Both the statements together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement I gives the cost of painting, which requires knowing the surface area, but doesn't provide enough info to find the radius without knowing the total cost or surface area. Statement II provides the volume of the cube (2^3 = 8), which equals the volume of the sphere (4/3 * pi * r^3 = 8). This allows solving for r. Thus, II alone is sufficient.

AI explanation

Statement II provides the side length of the cube as 2 m, giving a volume of 2^3 = 8 m3. When the cube is melted to form a sphere, the volume remains the same, so using the sphere volume formula (4/3) * pi * r^3 = 8 allows you to solve for the radius. Statement I only gives the rate of painting, which is insufficient without the total cost. Therefore, the question can be answered by using statement II alone, but cannot be answered by using statement I alone.

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