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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.
Solution
We have,
Edges of the cubes : a1 = 3 cm, a2 = 4 cm and a3 = 5 cm
Let the edge of the new cube be a.
Now,
` "Volume of the new cube" = a_1^3 +a_2^3+a_3^3`
`=>a^3 = 3^3 + 4^3 + 5^3`
⇒ a3 = 27 + 64 + 125
⇒ a3 = 216
`⇒ a = root(3)(216)`
∴ a = 6 cm
So, the edge of the new cube so formed is 6 cm.
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