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.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 Â = 60 3
Or a 3 Â = (60/6) 3
Or, a = 10
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