Multiple choice

$A metallic cylinder and a metallic cone are melted to form a solid sphere. Radius of cylinder and cone are in the ratio 3: 2 respectively. What is the radius of sphere? (Take (\pi = \frac{22}{7})$ Statement I: Height of cylinder and cone are in the ratio 4: 5 respectively and sum of volume of cylinder and cone is 39424 cm3. Statement II: Volume of cone is 27104 cm3 less than the volume of cylinder and sum of their heights is 54 cm. Statement III: Curved surface area of cylinder is 3168 cm2 and its radius and height are in the ratio 7: 8 respectively.

  1. Only statement I alone is sufficient

  2. Either statement II alone is sufficient or statement I and III together are sufficient.

  3. Either statement I alone is sufficient or statement II and III together are sufficient.

  4. Any of the two statements together are sufficient/

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I alone is sufficient because it provides the height ratio (4:5), radius ratio (3:2 given), and total volume (39424 cm³). Using volume formulas V = πr²h (cylinder) and V = (1/3)πr²h (cone), we can set up equations to solve for the actual radii and heights, then equate total volume to sphere volume (4/3)πR³. Statement II and III together also work: II gives volume difference and height sum, III gives curved surface area and radius:height ratio for the cylinder.

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