ഒരു ഘനത്തിന്റെ അരിക് 2 സെന്റിമീറ്റർ വർദ്ധിപ്പിച്ചാൽ, വ്യാപ്തം  488 സെന്റിമീറ്റർ3 വർദ്ധിക്കും. അപ്പോൾ ഘനത്തിന്റെ ഓരോ അരികുകളുടെയും നീളം എന്തായിരിക്കും?

This question was previously asked in
RRB ALP Previous Paper 8 (Held On: 13 Aug 2018 Shift 3)
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  1. 8 cm 
  2. 6 cm 
  3. 9 cm 
  4. 7 cm 

Answer (Detailed Solution Below)

Option 1 : 8 cm 
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Detailed Solution

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ഘനത്തിന്റെ നീളം x cm ആണ്.

⇒  2 സെന്റിമീറ്ററിന് ശേഷമുള്ള നീളം = x + 2 മീ

⇒ പ്രാരംഭ വ്യാപ്തം = x3

⇒ വശം വർധിച്ചതിന് ശേഷമുള്ള വ്യാപ്തം  = (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 cm

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