Multiple choice

The radius of a wire is decreased to one third. If volume remains the same, length will increase by. किसी तार की त्रिज्या एक-तिहाई कम कर दी जाती है तो लंबाई को कितना बढ़ा दें कि आयतन में कोई परिवर्तन न हो |

  1. 3 times/गुना

  2. 1 times/गुना

  3. 9 times/गुना

  4. 6 times/गुना
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C Correct answer
Explanation

Volume of a cylinder (wire) = πr²h. If volume remains constant and radius decreases to 1/3, we have: πr²h = π(r/3)² × h'. This gives r²h = (r²/9)h', so h' = 9h. The length increases by 9 times to maintain the same volume when radius is reduced to one-third.

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