একটি ঘনকের পৃষ্ঠের ক্ষেত্রফল 864 বর্গসেমি হলে কিউবের আয়তন কত?

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SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 2)
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  1. 1728 ঘনসেমি 
  2. 2197 ঘনসেমি 
  3. 1331 ঘনসেমি 
  4. 729 ঘনসেমি 

Answer (Detailed Solution Below)

Option 1 : 1728 ঘনসেমি 
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Detailed Solution

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প্রদত্ত:

একটি ঘনকের পৃষ্ঠের ক্ষেত্রফল 864বর্গসেমি 

অনুসৃত ধারণা:

1. একটি ঘনকের পৃষ্ঠের ক্ষেত্রফল = 6 × (পার্শ্ব)2

2. একটি ঘনকের আয়তন = (পার্শ্ব)3

গণনা:

ধরি, কিউবের প্রতিটি বাহুর পরিমাপ A সেমি  

প্রশ্ন অনুযায়ী,

6A2 = 864

⇒ A2 = 144

⇒ A = 12

এখন, ঘনকের আয়তন = 123 = 1728 ঘনসেমি 

∴ ঘনকের আয়তন 1728 ঘনসেমি 

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