একটি ঘনকের প্রান্ত 2 সেমি বৃদ্ধি করা হলে এর আয়তন 488 ঘনসেমি বৃদ্ধি পাবে। ঘনকের প্রতিটি প্রান্তের দৈর্ঘ্য কত?

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RRB ALP Previous Paper 8 (Held On: 13 Aug 2018 Shift 3)
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  1. 8 সেমি
  2. 6 সেমি
  3. 9 সেমি
  4. 7 সেমি

Answer (Detailed Solution Below)

Option 1 : 8 সেমি
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ধরা যাক ঘনকের দৈর্ঘ্যটি হল x সেমি 

⇒ 2 সেমি বৃদ্ধির পরে দৈর্ঘ্য হবে = x + 2 সেমি

⇒ প্রাথমিক আয়তন = x3

⇒ প্রান্তের দৈর্ঘ্য বৃদ্ধির পরে আয়তন= (x + 2)3

⇒ (x + 2)3 – x3 = 488

⇒ x3 + 6x2 + 12x + 8 – x3 = 488

⇒ 6x2 + 12x – 480 = 0

⇒ x2 + 2x – 80 = 0

⇒ (x – 8) (x + 10) = 0

⇒ x = 8, -10

⇒ x = 8 সেমি

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