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Question
Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast into a single large cube. Find the edge of the new cube formed.
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Solution
We have,
Edges of the new cubes `= a_1^3 + a_2^3 + a_3^3`
⇒ a3 = a3 + 43 + 53
⇒ a3 = 27 + 64 + 125
⇒ a3 = 216
`⇒ a^3 = root(3)(216)`
∴ a = 6 cm
So, the edge of the new cube so formed is 6 cm.
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