Multiple choice

A cone is 14.4 m. high and the radius of its base is 3.6 m.It is melted and recast into a sphere. The diameter of the sphere is एक शंकु 14.4 मी ऊँचा है और इसके आधार की त्रिज्या 3.6 मी है | इसे पिघलाकर एक गोला बनाया जाता है | गोले का व्यास है

  1. 6 m./मी

  2. 6.4 m./मी

  3. 7 m./मी

  4. 7.2 m./मी
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D Correct answer
Explanation

Volume of cone = (1/3)πr²h = (1/3) × π × 3.6² × 14.4. When melted and recast, volume of sphere = (4/3)πR³. Equating volumes: (1/3) × π × 3.6² × 14.4 = (4/3)πR³. Cancelling (1/3)π: 3.6² × 14.4 = 4R³. 12.96 × 14.4 = 4R³, so 186.624 = 4R³, giving R³ = 46.656 and R = 3.6 m. Diameter = 2R = 7.2 m.

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