গোলকের আয়তন গোলার্ধের আয়তনের সমান। তাদের ব্যাসার্ধের অনুপাতটি সন্ধান করুন।

  1. 1: √3
  2. 1: √2
  3. 1: \(\sqrt[3]{4}\)
  4. 1: \(\sqrt[3]{2}\)

Answer (Detailed Solution Below)

Option 4 : 1: \(\sqrt[3]{2}\)
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Detailed Solution

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সূত্র:

গোলকের আয়তন = [4/3] × πr3

গোলার্ধের আয়তন = [2/3] × πr3

গণনা:

ধরা যাক, গোলক এবং গোলার্ধের ব্যাসার্ধটি হল যথাক্রমে R এবং r 

প্রশ্ন অনুযায়ী

[4/3] × π × R3 = [2/3] × π × r3

⇒ R3/r3 = 1/2

⇒ R : r = 1 : ∛2

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