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    Question

    24 cubes having sides equal to a cm each, and 24 more cubes

    having sides equal to 2a cm each are melted to form a single cube such that diagonal of the new cube formed is 60√3 cm. Find the value of a.
    A 8 Correct Answer Incorrect Answer
    B 6 Correct Answer Incorrect Answer
    C 10 Correct Answer Incorrect Answer
    D Cannot be determined Correct Answer Incorrect Answer

    Solution

    According to the question,
    Each side of the bigger cube formed = 60√3/√3 = 60 cm (Diagonal = √3 × side)
    Therefore, 24 × (a) 3  + 24 × (2a) 3  = 60 3
    Or, 24a 3  × (1 3  + 2 3 ) = (60 × 60 × 60)
    Or, 24a 3  (1 + 8) = (60 × 60 × 60)
    Or, 216a 3   = 60 3
    Or a 3  = (60/6) 3
    Or, a = 10

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